The P versus NP–complete dichotomy of some challenging problems in graph theory

The Clay Mathematics Institute has selected seven Millennium Problems to motivate research on important classic questions that have resisted solution over the years. Among them is the central problem in theoretical computer science: the P versus NP problem, which aims to classify the possible existe...

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Published in:Discrete Applied Mathematics Vol. 160; no. 18; pp. 2681 - 2693
Main Author: de Figueiredo, Celina M.H.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2012
Subjects:
Analysis of algorithms and problem complexity
Classification
Combinatorial analysis
Dichotomies
Graph algorithms
Graph theory
Graphs
Mathematical models
Optimization
Partitions
Structural characterization of types of graphs
Analysis of algorithms and problem complexity
Graph algorithms
Structural characterization of types of graphs
ISSN:0166-218X, 1872-6771
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Abstract The Clay Mathematics Institute has selected seven Millennium Problems to motivate research on important classic questions that have resisted solution over the years. Among them is the central problem in theoretical computer science: the P versus NP problem, which aims to classify the possible existence of efficient solutions to combinatorial and optimization problems. The main goal is to determine whether there are questions whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure. In this context, it is important to determine precisely what facet of a problem makes it NP–complete. We shall discuss classes of problems for which dichotomy results do exist: every problem in the class is classified into polynomial or NP–complete. We shall discuss our contribution through the classification of some long-standing problems in important areas of graph theory: perfect graphs, intersection graphs, and structural characterization of graph classes. More precisely, we have shown that Chvátal’s skew partition is polynomial and that Roberts–Spencer’s clique graph is NP–complete. We have also solved the dichotomy for Golumbic–Kaplan–Shamir’s sandwich problem. We shall describe two examples where we can determine the full dichotomy: the edge-colouring problem for graphs with no cycle with a unique chord and the three nonempty part sandwich problem. Some open problems are discussed: the stubborn problem for list partition, the chromatic index of chordal graphs, and the recognition of split clique graphs.
AbstractList The Clay Mathematics Institute has selected seven Millennium Problems to motivate research on important classic questions that have resisted solution over the years. Among them is the central problem in theoretical computer science: the P versus NP problem, which aims to classify the possible existence of efficient solutions to combinatorial and optimization problems. The main goal is to determine whether there are questions whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure. In this context, it is important to determine precisely what facet of a problem makes it NP–complete. We shall discuss classes of problems for which dichotomy results do exist: every problem in the class is classified into polynomial or NP–complete. We shall discuss our contribution through the classification of some long-standing problems in important areas of graph theory: perfect graphs, intersection graphs, and structural characterization of graph classes. More precisely, we have shown that Chvátal’s skew partition is polynomial and that Roberts–Spencer’s clique graph is NP–complete. We have also solved the dichotomy for Golumbic–Kaplan–Shamir’s sandwich problem. We shall describe two examples where we can determine the full dichotomy: the edge-colouring problem for graphs with no cycle with a unique chord and the three nonempty part sandwich problem. Some open problems are discussed: the stubborn problem for list partition, the chromatic index of chordal graphs, and the recognition of split clique graphs.
The Clay Mathematics Institute has selected seven Millennium Problems to motivate research on important classic questions that have resisted solution over the years. Among them is the central problem in theoretical computer science: the P versus NP problem, which aims to classify the possible existence of efficient solutions to combinatorial and optimization problems. The main goal is to determine whether there are questions whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure. In this context, it is important to determine precisely what facet of a problem makes it NP-complete. We shall discuss classes of problems for which dichotomy results do exist: every problem in the class is classified into polynomial or NP-complete. We shall discuss our contribution through the classification of some long-standing problems in important areas of graph theory: perfect graphs, intersection graphs, and structural characterization of graph classes. More precisely, we have shown that Chvatal's skew partition is polynomial and that Roberts-Spencer's clique graph is NP-complete. We have also solved the dichotomy for Golumbic-Kaplan-Shamir's sandwich problem. We shall describe two examples where we can determine the full dichotomy: the edge-colouring problem for graphs with no cycle with a unique chord and the three nonempty part sandwich problem. Some open problems are discussed: the stubborn problem for list partition, the chromatic index of chordal graphs, and the recognition of split clique graphs.
Author de Figueiredo, Celina M.H.
Author_xml – sequence: 1
  givenname: Celina M.H.
  surname: de Figueiredo
  fullname: de Figueiredo, Celina M.H.
  email: celina@cos.ufrj.br, cmhfig@gmail.com
  organization: COPPE, Universidade Federal do Rio de Janeiro, Brazil
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Cites_doi 10.1137/S0895480191223191
10.1016/j.disc.2007.06.004
10.1016/j.tcs.2007.07.046
10.1016/j.tcs.2009.12.018
10.1016/S0020-0190(98)00076-3
10.1016/j.dam.2004.02.008
10.1016/0095-8956(85)90049-8
10.1002/jgt.20405
10.37236/1551
10.1016/S0166-218X(00)00197-9
10.1137/S0895480100384055
10.1007/s00493-005-0012-8
10.1007/s00373-003-0540-1
10.1016/0095-8956(71)90070-0
10.1016/S0166-218X(03)00369-X
10.1016/S0166-218X(98)00116-4
10.1017/S030500410006610X
10.1137/060666238
10.1006/jagm.1995.1047
10.1016/j.disc.2009.11.030
10.1137/0210055
10.1002/jgt.20165
10.1016/0196-6774(85)90012-4
10.1016/j.dam.2006.03.023
10.1016/S0021-9800(68)80055-9
10.1002/1097-0118(200012)35:4<257::AID-JGT3>3.0.CO;2-4
10.1016/S0012-365X(97)00085-X
10.1016/S0166-218X(01)00246-3
10.1145/1562164.1562186
10.1016/j.dam.2010.03.015
10.1006/jagm.1999.1122
10.1016/j.tcs.2009.01.018
10.1002/jgt.3190160207
10.1016/j.dam.2007.05.054
10.1016/S0012-365X(97)00255-0
10.1016/j.endm.2010.05.085
10.1016/0020-0190(79)90002-4
10.1016/j.tcs.2005.12.010
10.1016/S0304-3975(96)00264-2
10.1016/S0166-218X(03)00379-2
10.1051/ita:2005008
10.1016/j.dam.2009.12.002
10.1137/0603021
10.1016/j.tcs.2007.04.007
10.1016/0012-365X(94)00296-U
10.1016/S0166-218X(97)00128-5
10.1002/jgt.3190050103
10.4007/annals.2006.164.51
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Keywords Analysis of algorithms and problem complexity
Graph algorithms
Structural characterization of types of graphs
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References Chudnovsky, Robertson, Seymour, Thomas (br000085) 2006; 164
Cerioli, Everett, de Figueiredo, Klein (br000060) 1998; 67
Bodlaender, de Figueiredo, Gutierrez, Kloks, Niedermeier (br000030) 2004; vol. 3059
Protti, Szwarcfiter (br000260) 2000; 35
Pizaña (br000240) 2004; 141
Cunningham (br000100) 1982; 3
Prisner (br000255) 1995; vol. 338
Ortiz Z, Maculan, Szwarcfiter (br000230) 1998; 82
Holyer (br000180) 1981; 10
de Figueiredo, Meidanis, de Mello (br000125) 2000; 32
Niessen (br000225) 2001; 8
J.L. Ramirez Alfonsin, B.A. Reed, Perfect Graphs, Wiley-Interscience Series in Discrete Mathematics and Optimization, Chichester, 2001.
de Figueiredo, Meidanis, de Mello (br000120) 1997; 181
Plantholt (br000245) 1981; 5
Fortnow (br000145) 2009; 52
Sritharan (br000305) 2008; 308
Kennedy, Reed (br000195) 2008; vol. 4535
Papadimitriou (br000235) 1994
Alcón, Gutierrez (br000005) 2004; 141
.
Hamelink (br000170) 1968; 5
Cameron, Eschen, Hoàng, Sritharan (br000055) 2007; 21
Dantas, de Figueiredo, Gravier, Klein (br000110) 2005; 39
Trotignon, Vušković (br000345) 2010; 63
Brandstädt, Le, Szymczak (br000040) 1998; 89
Gyárfás (br000165) 1987; 19
D.S. Johnson, NP-completeness columns. Available at
Berge, Chvátal (br000025) 1984; vol. 88
Simone, de Mello (br000285) 2006; 355
Klein, de Figueiredo (br000200) 1996; 119
Spinrad (br000295) 2003; vol. 19
de Figueiredo, Klein, Kohayakawa, Reed (br000130) 2000; 37
Reed (br000275) 2008; 156
Chudnovsky (br000080) 2006; 53
Feder, Hell, Klein, Motwani (br000115) 2003; 16
Szwarcfiter, Bornstein (br000310) 1994; 7
Machado, de Figueiredo, Vušković (br000205) 2010; 411
Szwarcfiter (br000320) 2003; vol. 11
Prisner (br000250) 1993; 14
Chen, Fu, Ko (br000065) 1995; 17
Chetwynd, Hilton (br000070) 1986; 100
McKee, McMorris (br000215) 1999
Brandstädt (br000035) 1996; 152
Barbosa, de Mello, Meidanis (br000020) 1998; 133
Garey, Johnson (br000150) 1979
Brandstädt, Le, Dragan, Szymczak (br000045) 2000; 105
B. Aspvall, F.M. Plass, R.E. Tarjan, A linear-time algorithm for testing the truth of certain quantified Boolean formulas, Inform. Process. Lett., 8, 121–123.
Simone, Galluccio (br000290) 2007; 389
de Figueiredo, Faria, Klein, Sritharan (br000140) 2007; 381
de Mello, Lucchesi, Szwarcfiter (br000220) 1998; 183
Chudnovsky, Cornuéjols, Liu, Seymour, Vušković (br000075) 2005; 25
de Figueiredo, Klein, Vušković (br000135) 2002; 121
Steffen (br000300) 1998; 188
Brandstädt, Le, Spinrad (br000050) 1999
Hoffman, Rodger (br000175) 1992; 16
Golumbic, Kaplan, Shamir (br000155) 1995; 19
West (br000350) 2001
Johnson (br000190) 1985; 6
Cook, Dantas, Eschen, Faria, de Figueiredo, Klein (br000095) 2010; 310
R.B. Teixeira, S. Dantas, C.M.H. de Figueiredo, The external constraint 4 nonempty part sandwich problem, in: Proc. of Congreso Latino-Iberoamericano de Investigacin Operativa, CLAIO 2008, Full Paper Discrete Appl. Math., in press
Teixeira, de Figueiredo (br000325) 2006; 154
Teixeira, Dantas, de Figueiredo (br000340) 2009; vol. 35
Szwarcfiter (br000315) 1997; 45
Roberts, Spencer (br000280) 1971; 10
Alcón, de Figueiredo, Faria, Gutierrez (br000010) 2009; 410
Teixeira, Dantas, de Figueiredo (br000330) 2010; 158
Dantas, Faria, de Figueiredo (br000105) 2004; 143
Machado, de Figueiredo (br000210) 2010; 36
Chvátal (br000090) 1985; 39
Randerath, Schiermeyer (br000270) 2004; 20
Gutierrez, Meidanis (br000160) 1998; vol. 1380
Machado (10.1016/j.dam.2010.12.014_br000210) 2010; 36
Reed (10.1016/j.dam.2010.12.014_br000275) 2008; 156
Brandstädt (10.1016/j.dam.2010.12.014_br000045) 2000; 105
de Figueiredo (10.1016/j.dam.2010.12.014_br000135) 2002; 121
Ortiz Z (10.1016/j.dam.2010.12.014_br000230) 1998; 82
Teixeira (10.1016/j.dam.2010.12.014_br000325) 2006; 154
Chudnovsky (10.1016/j.dam.2010.12.014_br000080) 2006; 53
Spinrad (10.1016/j.dam.2010.12.014_br000295) 2003; vol. 19
Simone (10.1016/j.dam.2010.12.014_br000290) 2007; 389
Brandstädt (10.1016/j.dam.2010.12.014_br000035) 1996; 152
de Figueiredo (10.1016/j.dam.2010.12.014_br000130) 2000; 37
Dantas (10.1016/j.dam.2010.12.014_br000110) 2005; 39
Fortnow (10.1016/j.dam.2010.12.014_br000145) 2009; 52
Brandstädt (10.1016/j.dam.2010.12.014_br000040) 1998; 89
Barbosa (10.1016/j.dam.2010.12.014_br000020) 1998; 133
Teixeira (10.1016/j.dam.2010.12.014_br000330) 2010; 158
Chvátal (10.1016/j.dam.2010.12.014_br000090) 1985; 39
Szwarcfiter (10.1016/j.dam.2010.12.014_br000310) 1994; 7
Gyárfás (10.1016/j.dam.2010.12.014_br000165) 1987; 19
Niessen (10.1016/j.dam.2010.12.014_br000225) 2001; 8
Johnson (10.1016/j.dam.2010.12.014_br000190) 1985; 6
Roberts (10.1016/j.dam.2010.12.014_br000280) 1971; 10
Berge (10.1016/j.dam.2010.12.014_br000025) 1984; vol. 88
McKee (10.1016/j.dam.2010.12.014_br000215) 1999
Papadimitriou (10.1016/j.dam.2010.12.014_br000235) 1994
Chen (10.1016/j.dam.2010.12.014_br000065) 1995; 17
Chetwynd (10.1016/j.dam.2010.12.014_br000070) 1986; 100
Pizaña (10.1016/j.dam.2010.12.014_br000240) 2004; 141
10.1016/j.dam.2010.12.014_br000015
10.1016/j.dam.2010.12.014_br000335
Cerioli (10.1016/j.dam.2010.12.014_br000060) 1998; 67
Prisner (10.1016/j.dam.2010.12.014_br000250) 1993; 14
Dantas (10.1016/j.dam.2010.12.014_br000105) 2004; 143
Alcón (10.1016/j.dam.2010.12.014_br000005) 2004; 141
Garey (10.1016/j.dam.2010.12.014_br000150) 1979
Klein (10.1016/j.dam.2010.12.014_br000200) 1996; 119
Feder (10.1016/j.dam.2010.12.014_br000115) 2003; 16
Golumbic (10.1016/j.dam.2010.12.014_br000155) 1995; 19
Hamelink (10.1016/j.dam.2010.12.014_br000170) 1968; 5
Protti (10.1016/j.dam.2010.12.014_br000260) 2000; 35
Machado (10.1016/j.dam.2010.12.014_br000205) 2010; 411
Chudnovsky (10.1016/j.dam.2010.12.014_br000075) 2005; 25
Sritharan (10.1016/j.dam.2010.12.014_br000305) 2008; 308
Holyer (10.1016/j.dam.2010.12.014_br000180) 1981; 10
Hoffman (10.1016/j.dam.2010.12.014_br000175) 1992; 16
West (10.1016/j.dam.2010.12.014_br000350) 2001
Trotignon (10.1016/j.dam.2010.12.014_br000345) 2010; 63
de Figueiredo (10.1016/j.dam.2010.12.014_br000120) 1997; 181
Brandstädt (10.1016/j.dam.2010.12.014_br000050) 1999
Cunningham (10.1016/j.dam.2010.12.014_br000100) 1982; 3
Kennedy (10.1016/j.dam.2010.12.014_br000195) 2008; vol. 4535
Szwarcfiter (10.1016/j.dam.2010.12.014_br000315) 1997; 45
10.1016/j.dam.2010.12.014_br000185
Steffen (10.1016/j.dam.2010.12.014_br000300) 1998; 188
Teixeira (10.1016/j.dam.2010.12.014_br000340) 2009; vol. 35
10.1016/j.dam.2010.12.014_br000265
Chudnovsky (10.1016/j.dam.2010.12.014_br000085) 2006; 164
de Mello (10.1016/j.dam.2010.12.014_br000220) 1998; 183
Plantholt (10.1016/j.dam.2010.12.014_br000245) 1981; 5
Cameron (10.1016/j.dam.2010.12.014_br000055) 2007; 21
Bodlaender (10.1016/j.dam.2010.12.014_br000030) 2004; vol. 3059
Simone (10.1016/j.dam.2010.12.014_br000285) 2006; 355
de Figueiredo (10.1016/j.dam.2010.12.014_br000125) 2000; 32
de Figueiredo (10.1016/j.dam.2010.12.014_br000140) 2007; 381
Gutierrez (10.1016/j.dam.2010.12.014_br000160) 1998; vol. 1380
Prisner (10.1016/j.dam.2010.12.014_br000255) 1995; vol. 338
Randerath (10.1016/j.dam.2010.12.014_br000270) 2004; 20
Cook (10.1016/j.dam.2010.12.014_br000095) 2010; 310
Szwarcfiter (10.1016/j.dam.2010.12.014_br000320) 2003; vol. 11
Alcón (10.1016/j.dam.2010.12.014_br000010) 2009; 410
References_xml – volume: 39
  start-page: 133
  year: 2005
  end-page: 144
  ident: br000110
  article-title: Finding
  publication-title: Theor. Inform. Appl.
– volume: vol. 11
  start-page: 109
  year: 2003
  end-page: 136
  ident: br000320
  article-title: A survey on clique graphs
  publication-title: Recent Advances in Algorithms and Combinatorics
– volume: 310
  start-page: 1259
  year: 2010
  end-page: 1264
  ident: br000095
  article-title: vertex-set partition into nonempty parts
  publication-title: Discrete Math.
– volume: 52
  start-page: 78
  year: 2009
  end-page: 86
  ident: br000145
  article-title: The status of the P versus NP problem
  publication-title: Commun. ACM
– volume: 181
  start-page: 91
  year: 1997
  end-page: 106
  ident: br000120
  article-title: On edge-colouring indifference graphs
  publication-title: Theoret. Comput. Sci.
– year: 1979
  ident: br000150
  article-title: Computers and Intractability. A Guide to the Theory of NP-Completeness
– volume: 32
  start-page: 79
  year: 2000
  end-page: 91
  ident: br000125
  article-title: Local conditions for edge-coloring
  publication-title: J. Combin. Math. Combin. Comput.
– volume: 156
  start-page: 1150
  year: 2008
  end-page: 1156
  ident: br000275
  article-title: Skew partitions in perfect graphs
  publication-title: Discrete Appl. Math.
– reference: ).
– volume: 53
  start-page: 1
  year: 2006
  end-page: 55
  ident: br000080
  article-title: Berge trigraphs
  publication-title: J. Graph Theory
– volume: 121
  start-page: 73
  year: 2002
  end-page: 82
  ident: br000135
  article-title: The graph sandwich problem for 1-join composition is NP-complete
  publication-title: Discrete Appl. Math.
– volume: 10
  start-page: 102
  year: 1971
  end-page: 108
  ident: br000280
  article-title: A characterization of clique graphs
  publication-title: J. Combin. Theory Ser. B
– reference: D.S. Johnson, NP-completeness columns. Available at:
– year: 1999
  ident: br000215
  publication-title: Topics in Intersection Graph Theory
– volume: 67
  start-page: 31
  year: 1998
  end-page: 35
  ident: br000060
  article-title: The homogeneous set sandwich problem
  publication-title: Inform. Process. Lett.
– volume: vol. 3059
  start-page: 87
  year: 2004
  end-page: 99
  ident: br000030
  article-title: Simple max-cut for split-indifference graphs and graphs with few
  publication-title: Proc. of Third International Workshop on Experimental and Efficient Algorithms
– volume: 16
  start-page: 159
  year: 1992
  end-page: 163
  ident: br000175
  article-title: The chromatic index of complete multipartite graphs
  publication-title: J. Graph Theory
– volume: 5
  start-page: 45
  year: 1981
  end-page: 53
  ident: br000245
  article-title: The chromatic index of graphs with a spanning star
  publication-title: J. Graph Theory
– volume: 37
  start-page: 505
  year: 2000
  end-page: 521
  ident: br000130
  article-title: Finding skew partitions efficiently
  publication-title: J. Algorithms
– volume: 100
  start-page: 303
  year: 1986
  end-page: 317
  ident: br000070
  article-title: Star multigraphs with three vertices of maximum degree
  publication-title: Math. Proc. Cambridge Philos. Soc.
– volume: 10
  start-page: 718
  year: 1981
  end-page: 720
  ident: br000180
  article-title: The NP-completeness of edge-coloring
  publication-title: SIAM J. Comput.
– volume: 89
  start-page: 59
  year: 1998
  end-page: 73
  ident: br000040
  article-title: The complexity of some problems related to graph 3-colorability
  publication-title: Discrete Appl. Math.
– volume: vol. 88
  year: 1984
  ident: br000025
  publication-title: Topics on Perfect Graphs
– volume: 389
  start-page: 91
  year: 2007
  end-page: 99
  ident: br000290
  article-title: Edge-colouring of regular graphs of large degree
  publication-title: Theoret. Comput. Sci.
– volume: 154
  start-page: 1791
  year: 2006
  end-page: 1798
  ident: br000325
  article-title: The sandwich problem for cutsets: clique cutset,
  publication-title: Discrete Appl. Math.
– volume: 164
  start-page: 51
  year: 2006
  end-page: 229
  ident: br000085
  article-title: The strong perfect graph theorem
  publication-title: Ann. of Math.
– volume: 355
  start-page: 364
  year: 2006
  end-page: 370
  ident: br000285
  article-title: Edge-colouring of join graphs
  publication-title: Theoret. Comput. Sci.
– volume: 381
  start-page: 57
  year: 2007
  end-page: 67
  ident: br000140
  article-title: On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs
  publication-title: Theoret. Comput. Sci.
– volume: 19
  start-page: 413
  year: 1987
  end-page: 441
  ident: br000165
  article-title: Problems from the world surrounding perfect graphs
  publication-title: Zastos. Mat.
– volume: 411
  start-page: 1221
  year: 2010
  end-page: 1234
  ident: br000205
  article-title: Chromatic index of graphs with no cycle with a unique chord
  publication-title: Theoret. Comput. Sci.
– volume: vol. 1380
  start-page: 261
  year: 1998
  end-page: 272
  ident: br000160
  article-title: On the clique operator
  publication-title: Proc. of LATIN’98: Theoretical Informatics
– volume: 133
  start-page: 45
  year: 1998
  end-page: 55
  ident: br000020
  article-title: Local conditions for edge-colouring of cographs
  publication-title: Congr. Numer.
– volume: 7
  start-page: 331
  year: 1994
  end-page: 336
  ident: br000310
  article-title: Clique graphs of chordal graphs and path graphs
  publication-title: SIAM J. Discrete Math.
– volume: 141
  start-page: 3
  year: 2004
  end-page: 17
  ident: br000005
  article-title: Cliques and extended triangles. A necessary condition for planar clique graphs
  publication-title: Discrete Appl. Math.
– volume: 410
  start-page: 2072
  year: 2009
  end-page: 2083
  ident: br000010
  article-title: The complexity of clique graph recognition
  publication-title: Theoret. Comput. Sci.
– volume: vol. 4535
  start-page: 101
  year: 2008
  end-page: 107
  ident: br000195
  article-title: Fast skew partition recognition
  publication-title: Proc. of Computational Geometry and Graph Theory: International Conference
– volume: 21
  start-page: 900
  year: 2007
  end-page: 929
  ident: br000055
  article-title: The complexity of the list partition problem for graphs
  publication-title: SIAM J. Discrete Math.
– volume: 141
  start-page: 255
  year: 2004
  end-page: 261
  ident: br000240
  article-title: Distances and diameters on iterated clique graphs
  publication-title: Discrete Appl. Math.
– volume: vol. 35
  start-page: 9
  year: 2009
  end-page: 14
  ident: br000340
  article-title: Skew partition sandwich problem is NP-complete
  publication-title: Proc. of Latin-American Algorithms, Graphs and Optimization Symposium
– volume: 119
  start-page: 216
  year: 1996
  end-page: 222
  ident: br000200
  article-title: The NP-completeness of multi-partite cutset testing
  publication-title: Congr. Numer.
– volume: 152
  start-page: 47
  year: 1996
  end-page: 54
  ident: br000035
  article-title: Partitions of graphs into one or two independent sets and cliques
  publication-title: Discrete Math.
– volume: 5
  start-page: 192
  year: 1968
  end-page: 197
  ident: br000170
  article-title: A partial characterization of clique graphs
  publication-title: J. Combin. Theory Ser. B
– volume: 17
  start-page: 137
  year: 1995
  end-page: 146
  ident: br000065
  article-title: Total chromatic number and chromatic index of split graphs
  publication-title: J. Combin. Math. Combin. Comput.
– volume: 143
  start-page: 155
  year: 2004
  end-page: 165
  ident: br000105
  article-title: On decision and optimization
  publication-title: Discrete Appl. Math.
– year: 1999
  ident: br000050
  publication-title: Graph Classes: A Survey
– volume: 8
  start-page: #R7
  year: 2001
  ident: br000225
  article-title: How to find overfull subgraphs in graphs with large maximum degree
  publication-title: Electron. J. Combin.
– volume: 63
  start-page: 31
  year: 2010
  end-page: 67
  ident: br000345
  article-title: A structure theorem for graphs with no cycle with a unique chord and its consequences
  publication-title: J. Graph Theory
– volume: 19
  start-page: 449
  year: 1995
  end-page: 473
  ident: br000155
  article-title: Graph sandwich problems
  publication-title: J. Algorithms
– volume: 45
  start-page: 29
  year: 1997
  end-page: 32
  ident: br000315
  article-title: Recognizing clique-Helly graphs
  publication-title: Ars Combin.
– year: 2001
  ident: br000350
  article-title: Introduction to Graph Theory
– volume: 25
  start-page: 143
  year: 2005
  end-page: 186
  ident: br000075
  article-title: Recognizing Berge graphs
  publication-title: Combinatorica
– year: 1994
  ident: br000235
  article-title: Computational Complexity
– volume: 39
  start-page: 189
  year: 1985
  end-page: 199
  ident: br000090
  article-title: Star-cutsets and perfect graphs
  publication-title: J. Combin. Theory Ser. B
– volume: 3
  start-page: 214
  year: 1982
  end-page: 228
  ident: br000100
  article-title: Decomposition of directed graphs
  publication-title: SIAM J. Algebr. Discrete Methods
– volume: 183
  start-page: 247
  year: 1998
  end-page: 254
  ident: br000220
  article-title: On clique-complete graphs
  publication-title: Discrete Math.
– reference: J.L. Ramirez Alfonsin, B.A. Reed, Perfect Graphs, Wiley-Interscience Series in Discrete Mathematics and Optimization, Chichester, 2001.
– volume: 14
  start-page: 216
  year: 1993
  end-page: 220
  ident: br000250
  article-title: Hereditary clique-Helly graphs
  publication-title: J. Combin. Math. Combin. Comput.
– volume: 36
  start-page: 671
  year: 2010
  end-page: 678
  ident: br000210
  article-title: Total chromatic number of {square,unichord}-free graphs
  publication-title: Proc. of International Symposium on Combinatorial Optimization, ISCO 2010
– reference: .
– volume: vol. 338
  year: 1995
  ident: br000255
  publication-title: Graph Dynamics
– reference: B. Aspvall, F.M. Plass, R.E. Tarjan, A linear-time algorithm for testing the truth of certain quantified Boolean formulas, Inform. Process. Lett., 8, 121–123.
– volume: 35
  start-page: 257
  year: 2000
  end-page: 272
  ident: br000260
  article-title: Clique-inverse graphs of
  publication-title: J. Graph Theory
– volume: 16
  start-page: 449
  year: 2003
  end-page: 478
  ident: br000115
  article-title: List partitions
  publication-title: SIAM J. Discrete Math.
– volume: 308
  start-page: 2581
  year: 2008
  end-page: 2588
  ident: br000305
  article-title: Chordal bipartite completion of colored graphs
  publication-title: Discrete Math.
– volume: 158
  start-page: 1286
  year: 2010
  end-page: 1304
  ident: br000330
  article-title: The polynomial dichotomy for three nonempty part sandwich problems
  publication-title: Discrete Appl. Math.
– volume: 6
  start-page: 434
  year: 1985
  end-page: 451
  ident: br000190
  article-title: Graph restrictions and their effect
  publication-title: J. Algorithms
– volume: 20
  start-page: 1
  year: 2004
  end-page: 40
  ident: br000270
  article-title: Vertex colouring and forbidden subgraphs—a survey
  publication-title: Graphs Combin.
– volume: vol. 19
  year: 2003
  ident: br000295
  publication-title: Efficient Graph Representations
– volume: 105
  start-page: 39
  year: 2000
  end-page: 50
  ident: br000045
  article-title: On stable cutsets in graphs
  publication-title: Discrete Appl. Math.
– volume: 188
  start-page: 183
  year: 1998
  end-page: 203
  ident: br000300
  article-title: Classifications and characterizations of snarks
  publication-title: Discrete Math.
– reference: R.B. Teixeira, S. Dantas, C.M.H. de Figueiredo, The external constraint 4 nonempty part sandwich problem, in: Proc. of Congreso Latino-Iberoamericano de Investigacin Operativa, CLAIO 2008, Full Paper Discrete Appl. Math., in press (
– volume: 82
  start-page: 209
  year: 1998
  end-page: 217
  ident: br000230
  article-title: Characterizing and edge-colouring split-indifference graphs
  publication-title: Discrete Appl. Math.
– volume: 7
  start-page: 331
  year: 1994
  ident: 10.1016/j.dam.2010.12.014_br000310
  article-title: Clique graphs of chordal graphs and path graphs
  publication-title: SIAM J. Discrete Math.
  doi: 10.1137/S0895480191223191
– year: 1999
  ident: 10.1016/j.dam.2010.12.014_br000050
– volume: 308
  start-page: 2581
  year: 2008
  ident: 10.1016/j.dam.2010.12.014_br000305
  article-title: Chordal bipartite completion of colored graphs
  publication-title: Discrete Math.
  doi: 10.1016/j.disc.2007.06.004
– volume: 17
  start-page: 137
  year: 1995
  ident: 10.1016/j.dam.2010.12.014_br000065
  article-title: Total chromatic number and chromatic index of split graphs
  publication-title: J. Combin. Math. Combin. Comput.
– volume: 32
  start-page: 79
  year: 2000
  ident: 10.1016/j.dam.2010.12.014_br000125
  article-title: Local conditions for edge-coloring
  publication-title: J. Combin. Math. Combin. Comput.
– volume: 389
  start-page: 91
  year: 2007
  ident: 10.1016/j.dam.2010.12.014_br000290
  article-title: Edge-colouring of regular graphs of large degree
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2007.07.046
– volume: 411
  start-page: 1221
  year: 2010
  ident: 10.1016/j.dam.2010.12.014_br000205
  article-title: Chromatic index of graphs with no cycle with a unique chord
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2009.12.018
– volume: 67
  start-page: 31
  year: 1998
  ident: 10.1016/j.dam.2010.12.014_br000060
  article-title: The homogeneous set sandwich problem
  publication-title: Inform. Process. Lett.
  doi: 10.1016/S0020-0190(98)00076-3
– volume: 143
  start-page: 155
  year: 2004
  ident: 10.1016/j.dam.2010.12.014_br000105
  article-title: On decision and optimization (k,l)-graph sandwich problems
  publication-title: Discrete Appl. Math.
  doi: 10.1016/j.dam.2004.02.008
– year: 1994
  ident: 10.1016/j.dam.2010.12.014_br000235
– year: 2001
  ident: 10.1016/j.dam.2010.12.014_br000350
– volume: 39
  start-page: 189
  year: 1985
  ident: 10.1016/j.dam.2010.12.014_br000090
  article-title: Star-cutsets and perfect graphs
  publication-title: J. Combin. Theory Ser. B
  doi: 10.1016/0095-8956(85)90049-8
– volume: vol. 88
  year: 1984
  ident: 10.1016/j.dam.2010.12.014_br000025
– year: 1979
  ident: 10.1016/j.dam.2010.12.014_br000150
– volume: 63
  start-page: 31
  year: 2010
  ident: 10.1016/j.dam.2010.12.014_br000345
  article-title: A structure theorem for graphs with no cycle with a unique chord and its consequences
  publication-title: J. Graph Theory
  doi: 10.1002/jgt.20405
– volume: 8
  start-page: #R7
  year: 2001
  ident: 10.1016/j.dam.2010.12.014_br000225
  article-title: How to find overfull subgraphs in graphs with large maximum degree
  publication-title: Electron. J. Combin.
  doi: 10.37236/1551
– volume: 105
  start-page: 39
  year: 2000
  ident: 10.1016/j.dam.2010.12.014_br000045
  article-title: On stable cutsets in graphs
  publication-title: Discrete Appl. Math.
  doi: 10.1016/S0166-218X(00)00197-9
– volume: 16
  start-page: 449
  year: 2003
  ident: 10.1016/j.dam.2010.12.014_br000115
  article-title: List partitions
  publication-title: SIAM J. Discrete Math.
  doi: 10.1137/S0895480100384055
– volume: 25
  start-page: 143
  year: 2005
  ident: 10.1016/j.dam.2010.12.014_br000075
  article-title: Recognizing Berge graphs
  publication-title: Combinatorica
  doi: 10.1007/s00493-005-0012-8
– volume: 20
  start-page: 1
  year: 2004
  ident: 10.1016/j.dam.2010.12.014_br000270
  article-title: Vertex colouring and forbidden subgraphs—a survey
  publication-title: Graphs Combin.
  doi: 10.1007/s00373-003-0540-1
– volume: 10
  start-page: 102
  year: 1971
  ident: 10.1016/j.dam.2010.12.014_br000280
  article-title: A characterization of clique graphs
  publication-title: J. Combin. Theory Ser. B
  doi: 10.1016/0095-8956(71)90070-0
– volume: 141
  start-page: 3
  year: 2004
  ident: 10.1016/j.dam.2010.12.014_br000005
  article-title: Cliques and extended triangles. A necessary condition for planar clique graphs
  publication-title: Discrete Appl. Math.
  doi: 10.1016/S0166-218X(03)00369-X
– volume: 133
  start-page: 45
  year: 1998
  ident: 10.1016/j.dam.2010.12.014_br000020
  article-title: Local conditions for edge-colouring of cographs
  publication-title: Congr. Numer.
– volume: vol. 4535
  start-page: 101
  year: 2008
  ident: 10.1016/j.dam.2010.12.014_br000195
  article-title: Fast skew partition recognition
– volume: vol. 338
  year: 1995
  ident: 10.1016/j.dam.2010.12.014_br000255
– volume: 89
  start-page: 59
  year: 1998
  ident: 10.1016/j.dam.2010.12.014_br000040
  article-title: The complexity of some problems related to graph 3-colorability
  publication-title: Discrete Appl. Math.
  doi: 10.1016/S0166-218X(98)00116-4
– volume: 100
  start-page: 303
  year: 1986
  ident: 10.1016/j.dam.2010.12.014_br000070
  article-title: Star multigraphs with three vertices of maximum degree
  publication-title: Math. Proc. Cambridge Philos. Soc.
  doi: 10.1017/S030500410006610X
– volume: vol. 19
  year: 2003
  ident: 10.1016/j.dam.2010.12.014_br000295
– volume: 21
  start-page: 900
  year: 2007
  ident: 10.1016/j.dam.2010.12.014_br000055
  article-title: The complexity of the list partition problem for graphs
  publication-title: SIAM J. Discrete Math.
  doi: 10.1137/060666238
– volume: 19
  start-page: 449
  year: 1995
  ident: 10.1016/j.dam.2010.12.014_br000155
  article-title: Graph sandwich problems
  publication-title: J. Algorithms
  doi: 10.1006/jagm.1995.1047
– volume: 310
  start-page: 1259
  year: 2010
  ident: 10.1016/j.dam.2010.12.014_br000095
  article-title: 2K2 vertex-set partition into nonempty parts
  publication-title: Discrete Math.
  doi: 10.1016/j.disc.2009.11.030
– volume: 10
  start-page: 718
  year: 1981
  ident: 10.1016/j.dam.2010.12.014_br000180
  article-title: The NP-completeness of edge-coloring
  publication-title: SIAM J. Comput.
  doi: 10.1137/0210055
– volume: vol. 35
  start-page: 9
  year: 2009
  ident: 10.1016/j.dam.2010.12.014_br000340
  article-title: Skew partition sandwich problem is NP-complete
– volume: 53
  start-page: 1
  year: 2006
  ident: 10.1016/j.dam.2010.12.014_br000080
  article-title: Berge trigraphs
  publication-title: J. Graph Theory
  doi: 10.1002/jgt.20165
– volume: 6
  start-page: 434
  year: 1985
  ident: 10.1016/j.dam.2010.12.014_br000190
  article-title: Graph restrictions and their effect
  publication-title: J. Algorithms
  doi: 10.1016/0196-6774(85)90012-4
– volume: 154
  start-page: 1791
  year: 2006
  ident: 10.1016/j.dam.2010.12.014_br000325
  article-title: The sandwich problem for cutsets: clique cutset, k-star cutset
  publication-title: Discrete Appl. Math.
  doi: 10.1016/j.dam.2006.03.023
– volume: 5
  start-page: 192
  year: 1968
  ident: 10.1016/j.dam.2010.12.014_br000170
  article-title: A partial characterization of clique graphs
  publication-title: J. Combin. Theory Ser. B
  doi: 10.1016/S0021-9800(68)80055-9
– volume: 35
  start-page: 257
  year: 2000
  ident: 10.1016/j.dam.2010.12.014_br000260
  article-title: Clique-inverse graphs of K3-free and K4-free graphs
  publication-title: J. Graph Theory
  doi: 10.1002/1097-0118(200012)35:4<257::AID-JGT3>3.0.CO;2-4
– volume: 183
  start-page: 247
  year: 1998
  ident: 10.1016/j.dam.2010.12.014_br000220
  article-title: On clique-complete graphs
  publication-title: Discrete Math.
  doi: 10.1016/S0012-365X(97)00085-X
– volume: 19
  start-page: 413
  year: 1987
  ident: 10.1016/j.dam.2010.12.014_br000165
  article-title: Problems from the world surrounding perfect graphs
  publication-title: Zastos. Mat.
– volume: 121
  start-page: 73
  year: 2002
  ident: 10.1016/j.dam.2010.12.014_br000135
  article-title: The graph sandwich problem for 1-join composition is NP-complete
  publication-title: Discrete Appl. Math.
  doi: 10.1016/S0166-218X(01)00246-3
– volume: 119
  start-page: 216
  year: 1996
  ident: 10.1016/j.dam.2010.12.014_br000200
  article-title: The NP-completeness of multi-partite cutset testing
  publication-title: Congr. Numer.
– volume: 52
  start-page: 78
  year: 2009
  ident: 10.1016/j.dam.2010.12.014_br000145
  article-title: The status of the P versus NP problem
  publication-title: Commun. ACM
  doi: 10.1145/1562164.1562186
– volume: vol. 11
  start-page: 109
  year: 2003
  ident: 10.1016/j.dam.2010.12.014_br000320
  article-title: A survey on clique graphs
– ident: 10.1016/j.dam.2010.12.014_br000335
  doi: 10.1016/j.dam.2010.03.015
– volume: 37
  start-page: 505
  year: 2000
  ident: 10.1016/j.dam.2010.12.014_br000130
  article-title: Finding skew partitions efficiently
  publication-title: J. Algorithms
  doi: 10.1006/jagm.1999.1122
– volume: 410
  start-page: 2072
  year: 2009
  ident: 10.1016/j.dam.2010.12.014_br000010
  article-title: The complexity of clique graph recognition
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2009.01.018
– volume: 16
  start-page: 159
  year: 1992
  ident: 10.1016/j.dam.2010.12.014_br000175
  article-title: The chromatic index of complete multipartite graphs
  publication-title: J. Graph Theory
  doi: 10.1002/jgt.3190160207
– ident: 10.1016/j.dam.2010.12.014_br000185
– volume: 156
  start-page: 1150
  year: 2008
  ident: 10.1016/j.dam.2010.12.014_br000275
  article-title: Skew partitions in perfect graphs
  publication-title: Discrete Appl. Math.
  doi: 10.1016/j.dam.2007.05.054
– volume: 188
  start-page: 183
  year: 1998
  ident: 10.1016/j.dam.2010.12.014_br000300
  article-title: Classifications and characterizations of snarks
  publication-title: Discrete Math.
  doi: 10.1016/S0012-365X(97)00255-0
– volume: 36
  start-page: 671
  year: 2010
  ident: 10.1016/j.dam.2010.12.014_br000210
  article-title: Total chromatic number of {square,unichord}-free graphs
  publication-title: Electron. Notes Discrete Math.
  doi: 10.1016/j.endm.2010.05.085
– ident: 10.1016/j.dam.2010.12.014_br000015
  doi: 10.1016/0020-0190(79)90002-4
– volume: vol. 3059
  start-page: 87
  year: 2004
  ident: 10.1016/j.dam.2010.12.014_br000030
  article-title: Simple max-cut for split-indifference graphs and graphs with few P4’s
– volume: 355
  start-page: 364
  year: 2006
  ident: 10.1016/j.dam.2010.12.014_br000285
  article-title: Edge-colouring of join graphs
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2005.12.010
– volume: 181
  start-page: 91
  year: 1997
  ident: 10.1016/j.dam.2010.12.014_br000120
  article-title: On edge-colouring indifference graphs
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/S0304-3975(96)00264-2
– volume: 141
  start-page: 255
  year: 2004
  ident: 10.1016/j.dam.2010.12.014_br000240
  article-title: Distances and diameters on iterated clique graphs
  publication-title: Discrete Appl. Math.
  doi: 10.1016/S0166-218X(03)00379-2
– volume: 39
  start-page: 133
  year: 2005
  ident: 10.1016/j.dam.2010.12.014_br000110
  article-title: Finding H-partition problems
  publication-title: Theor. Inform. Appl.
  doi: 10.1051/ita:2005008
– volume: 158
  start-page: 1286
  year: 2010
  ident: 10.1016/j.dam.2010.12.014_br000330
  article-title: The polynomial dichotomy for three nonempty part sandwich problems
  publication-title: Discrete Appl. Math.
  doi: 10.1016/j.dam.2009.12.002
– ident: 10.1016/j.dam.2010.12.014_br000265
– volume: 3
  start-page: 214
  year: 1982
  ident: 10.1016/j.dam.2010.12.014_br000100
  article-title: Decomposition of directed graphs
  publication-title: SIAM J. Algebr. Discrete Methods
  doi: 10.1137/0603021
– volume: 381
  start-page: 57
  year: 2007
  ident: 10.1016/j.dam.2010.12.014_br000140
  article-title: On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2007.04.007
– volume: 152
  start-page: 47
  year: 1996
  ident: 10.1016/j.dam.2010.12.014_br000035
  article-title: Partitions of graphs into one or two independent sets and cliques
  publication-title: Discrete Math.
  doi: 10.1016/0012-365X(94)00296-U
– volume: 82
  start-page: 209
  year: 1998
  ident: 10.1016/j.dam.2010.12.014_br000230
  article-title: Characterizing and edge-colouring split-indifference graphs
  publication-title: Discrete Appl. Math.
  doi: 10.1016/S0166-218X(97)00128-5
– volume: 5
  start-page: 45
  year: 1981
  ident: 10.1016/j.dam.2010.12.014_br000245
  article-title: The chromatic index of graphs with a spanning star
  publication-title: J. Graph Theory
  doi: 10.1002/jgt.3190050103
– volume: vol. 1380
  start-page: 261
  year: 1998
  ident: 10.1016/j.dam.2010.12.014_br000160
  article-title: On the clique operator
– volume: 14
  start-page: 216
  year: 1993
  ident: 10.1016/j.dam.2010.12.014_br000250
  article-title: Hereditary clique-Helly graphs
  publication-title: J. Combin. Math. Combin. Comput.
– year: 1999
  ident: 10.1016/j.dam.2010.12.014_br000215
– volume: 164
  start-page: 51
  year: 2006
  ident: 10.1016/j.dam.2010.12.014_br000085
  article-title: The strong perfect graph theorem
  publication-title: Ann. of Math.
  doi: 10.4007/annals.2006.164.51
– volume: 45
  start-page: 29
  year: 1997
  ident: 10.1016/j.dam.2010.12.014_br000315
  article-title: Recognizing clique-Helly graphs
  publication-title: Ars Combin.
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Snippet The Clay Mathematics Institute has selected seven Millennium Problems to motivate research on important classic questions that have resisted solution over the...
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SubjectTerms Analysis of algorithms and problem complexity
Classification
Combinatorial analysis
Dichotomies
Graph algorithms
Graph theory
Graphs
Mathematical models
Optimization
Partitions
Structural characterization of types of graphs
Title The P versus NP–complete dichotomy of some challenging problems in graph theory
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