An exact algorithm for the adjacent vertex distinguishing sum edge coloring problem
In this work we define the adjacent vertex distinguishing sum edge coloring problem. This problem consists of finding an assignment of colors to the edges of a graph with the following constraints: every pair of adjacent edges must have a different color, and every pair of adjacent vertices must not...
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| Vydáno v: | Discrete Applied Mathematics Ročník 371; s. 80 - 98 |
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| Jazyk: | angličtina |
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Elsevier B.V
15.08.2025
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| ISSN: | 0166-218X |
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| Abstract | In this work we define the adjacent vertex distinguishing sum edge coloring problem. This problem consists of finding an assignment of colors to the edges of a graph with the following constraints: every pair of adjacent edges must have a different color, and every pair of adjacent vertices must not have the same set of colors assigned to the edges incident to each. The goal is to minimize the sum of the colors in an edge coloring that satisfies these constraints. This problem is a special case of a large family of problems known as graph labeling, which is a widely used and very popular set of tools to build abstract models for problems that arise in everyday life.
Some variants of graph labeling problems have been successfully addressed with mixed-integer linear programming (MIP) techniques based on a polyhedral characterization of the set of feasible solutions. We use this approach to develop a Branch and Cut algorithm to solve the problem.
We propose two MIP models that are computationally evaluated to choose the most promising one and continue with a polyhedral study. This analysis aims to characterize valid inequalities that strengthen the formulation in the hope of improving the algorithm’s performance. These inequalities are added on demand as cutting planes using exact and heuristic separation algorithms. Additionally, we considered the use of an initial heuristic and a specific branching strategy.
The results show that the algorithm developed allows us to solve instances that were unsolvable using general-purpose solvers. Our polyhedral study and the addition of cutting planes have proved to be crucial factors in solving the most challenging instances. |
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| AbstractList | In this work we define the adjacent vertex distinguishing sum edge coloring problem. This problem consists of finding an assignment of colors to the edges of a graph with the following constraints: every pair of adjacent edges must have a different color, and every pair of adjacent vertices must not have the same set of colors assigned to the edges incident to each. The goal is to minimize the sum of the colors in an edge coloring that satisfies these constraints. This problem is a special case of a large family of problems known as graph labeling, which is a widely used and very popular set of tools to build abstract models for problems that arise in everyday life.
Some variants of graph labeling problems have been successfully addressed with mixed-integer linear programming (MIP) techniques based on a polyhedral characterization of the set of feasible solutions. We use this approach to develop a Branch and Cut algorithm to solve the problem.
We propose two MIP models that are computationally evaluated to choose the most promising one and continue with a polyhedral study. This analysis aims to characterize valid inequalities that strengthen the formulation in the hope of improving the algorithm’s performance. These inequalities are added on demand as cutting planes using exact and heuristic separation algorithms. Additionally, we considered the use of an initial heuristic and a specific branching strategy.
The results show that the algorithm developed allows us to solve instances that were unsolvable using general-purpose solvers. Our polyhedral study and the addition of cutting planes have proved to be crucial factors in solving the most challenging instances. |
| Author | Méndez-Díaz, Isabel Zabala, Paula Curcio, Brian |
| Author_xml | – sequence: 1 givenname: Brian surname: Curcio fullname: Curcio, Brian email: bcurcio@dc.uba.ar – sequence: 2 givenname: Isabel surname: Méndez-Díaz fullname: Méndez-Díaz, Isabel email: imendez@dc.uba.ar – sequence: 3 givenname: Paula surname: Zabala fullname: Zabala, Paula email: pzabala@dc.uba.ar |
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| Cites_doi | 10.1137/S0895480102414107 10.1007/s00373-006-0671-2 10.1016/j.dam.2014.11.028 10.1155/S0161171204306216 10.1016/S0166-218X(02)00249-4 10.1287/moor.7.1.67 10.1137/0214054 10.1016/j.disc.2020.112014 10.25080/TCWV9851 10.1016/S0012-365X(00)00428-3 10.1016/j.dam.2015.12.005 10.1016/j.jctb.2005.04.002 10.1007/s10878-021-00807-0 10.1016/0167-6377(93)90043-G 10.1016/j.dam.2020.08.031 10.54286/ikjm.972238 10.1016/j.aml.2011.05.038 10.1007/s10479-018-2977-x 10.6028/jres.069B.013 10.1016/j.endm.2017.10.047 10.1137/18M1200427 10.1016/j.dam.2023.05.010 10.1016/j.ipl.2009.02.006 10.1016/j.disc.2004.12.027 10.7151/dmgt.1556 10.1006/jctb.1998.1884 10.1016/0012-365X(95)00102-3 10.1016/j.dam.2008.04.002 10.1016/0167-6377(91)90003-8 10.1142/S2661335222500010 10.1016/S0012-365X(01)00287-4 10.1016/j.disopt.2018.12.001 10.1002/(SICI)1097-0118(199710)26:2<73::AID-JGT2>3.0.CO;2-C 10.1016/j.dam.2016.10.028 10.7151/dmgt.1050 10.1007/s10878-008-9178-5 10.1016/j.dam.2022.01.003 10.1023/B:JOCO.0000021940.40066.0c 10.1016/j.dam.2009.04.020 10.1016/j.disc.2019.01.024 10.1016/S0020-0190(00)00072-7 10.3390/math11102233 10.1016/j.dam.2013.09.025 10.1016/S0893-9659(02)80015-5 |
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| References | Bazgan, Harkat-Benhamdine, Li, Woźniak (b6) 1999; 75 Bu, Lih, Wang (b9) 2011; 31 Joret, Lochet (b28) 2020; 34 Sun, Yu, Li (b48) 2023; 337 Mehrotra, Trick (b36) 2007 Zhou, Nishizeki (b54) 2001 Hu, Wang, Wu, Yang, Yu (b26) 2019; 342 Delle Donne, Furini, Malaguti, Wolfler Calvo (b18) 2021; 303 Gong, Zhang (b23) 2023; 11 Tian, Wang (b49) 2015; 185 Mitchem, Morriss, Schmeichel (b37) 1997; 17 Padberg, Rao (b43) 1982; 7 Marx (b35) 2009; 157 Bazgan, Harkat-Benhamdine, Li, Woźniak (b7) 2001; 236 Shanthakumari (b46) 2018 Curcio (b16) 2021 Petrosyan, Kamalian (b44) 2014; 165 Chen, Guo (b13) 2009; 109 Borghini, Méndez-Díaz, Zabala (b8) 2020; 286 Cheng, Wang, Wang (b14) 2022; 313 Hatami (b25) 2005; 95 Padberg, Rao (b42) 1982; 7 Chang, Hu, Wang, Yu (b12) 2020; 343 Wang, Wang (b52) 2011; 24 Balister, Gyori, Lehel, Schelp (b5) 2007; 21 Aric A. Hagberg, Daniel A. Schult, Pieter J. Swart, Exploring Network Structure, Dynamics, and Function using NetworkX, in: Gaël Varoquaux, Travis Vaught, Jarrod Millman (Eds.), Proceedings of the 7th Python in Science Conference, Pasadena, CA USA, 2008, pp. 11–15. Balister, Bollobás, Schelp (b4) 2002; 252 Kubicka, Schwenk (b31) 1989 Giaro, Kubale (b22) 2000; 75 Zhou, Nishizeki (b55) 2004; 8 Letchford, Reinelt, Theis (b33) 2004; 3064 Johnson, Trick (b27) 1996 Wang, Wang (b51) 2010; 19 Favaron, Li, Schelp (b21) 1996; 159 Coffman, Garey, Johnson, LaPaugh (b15) 1985; 14 Naveen (b38) 2021; 3 Salavatipour (b45) 2003; 127 Liu, Xu (b34) 2022; 43 Lee, Leung (b32) 1993; 13 Cardinal, Ravelomanana, Valencia-Pabon (b11) 2010; 158 Aigner, Triesch (b1) 1990 Edmonds (b19) 1965; 69B Koch, Marenco (b29) 2019; 32 shanthakumari, Begam (b47) 2021 Naveen (b39) 2021; 13 Vizing (b50) 1964; 3 Kubicka (b30) 2004; 2004 Nemhauser, Park (b40) 1991; 10 Edwards, Horňák, Woźniak (b20) 2006; 22 Zhang, Liu, Wang (b53) 2002; 15 Burris, Schelp (b10) 1997; 26 Omai, de Almeida, Sasaki (b41) 2017; 62 Dehghan, Mollahajiaghaei (b17) 2017; 218 Axenovich, Harant, Przybyło, Soták, Voigt, Weidelich (b3) 2016; 205 Akbari, Bidkhori, Nosrati (b2) 2006; 306 Edwards (10.1016/j.dam.2025.03.029_b20) 2006; 22 Naveen (10.1016/j.dam.2025.03.029_b38) 2021; 3 Salavatipour (10.1016/j.dam.2025.03.029_b45) 2003; 127 Koch (10.1016/j.dam.2025.03.029_b29) 2019; 32 Joret (10.1016/j.dam.2025.03.029_b28) 2020; 34 Letchford (10.1016/j.dam.2025.03.029_b33) 2004; 3064 shanthakumari (10.1016/j.dam.2025.03.029_b47) 2021 Akbari (10.1016/j.dam.2025.03.029_b2) 2006; 306 Johnson (10.1016/j.dam.2025.03.029_b27) 1996 Favaron (10.1016/j.dam.2025.03.029_b21) 1996; 159 Giaro (10.1016/j.dam.2025.03.029_b22) 2000; 75 Tian (10.1016/j.dam.2025.03.029_b49) 2015; 185 Curcio (10.1016/j.dam.2025.03.029_b16) 2021 Kubicka (10.1016/j.dam.2025.03.029_b31) 1989 Aigner (10.1016/j.dam.2025.03.029_b1) 1990 Bu (10.1016/j.dam.2025.03.029_b9) 2011; 31 Zhang (10.1016/j.dam.2025.03.029_b53) 2002; 15 Mehrotra (10.1016/j.dam.2025.03.029_b36) 2007 Zhou (10.1016/j.dam.2025.03.029_b54) 2001 Hu (10.1016/j.dam.2025.03.029_b26) 2019; 342 Bazgan (10.1016/j.dam.2025.03.029_b7) 2001; 236 Hatami (10.1016/j.dam.2025.03.029_b25) 2005; 95 Dehghan (10.1016/j.dam.2025.03.029_b17) 2017; 218 Delle Donne (10.1016/j.dam.2025.03.029_b18) 2021; 303 Cardinal (10.1016/j.dam.2025.03.029_b11) 2010; 158 Wang (10.1016/j.dam.2025.03.029_b52) 2011; 24 Omai (10.1016/j.dam.2025.03.029_b41) 2017; 62 Balister (10.1016/j.dam.2025.03.029_b5) 2007; 21 Naveen (10.1016/j.dam.2025.03.029_b39) 2021; 13 Vizing (10.1016/j.dam.2025.03.029_b50) 1964; 3 Bazgan (10.1016/j.dam.2025.03.029_b6) 1999; 75 Chen (10.1016/j.dam.2025.03.029_b13) 2009; 109 Lee (10.1016/j.dam.2025.03.029_b32) 1993; 13 Zhou (10.1016/j.dam.2025.03.029_b55) 2004; 8 10.1016/j.dam.2025.03.029_b24 Balister (10.1016/j.dam.2025.03.029_b4) 2002; 252 Kubicka (10.1016/j.dam.2025.03.029_b30) 2004; 2004 Burris (10.1016/j.dam.2025.03.029_b10) 1997; 26 Chang (10.1016/j.dam.2025.03.029_b12) 2020; 343 Coffman (10.1016/j.dam.2025.03.029_b15) 1985; 14 Liu (10.1016/j.dam.2025.03.029_b34) 2022; 43 Padberg (10.1016/j.dam.2025.03.029_b42) 1982; 7 Gong (10.1016/j.dam.2025.03.029_b23) 2023; 11 Padberg (10.1016/j.dam.2025.03.029_b43) 1982; 7 Axenovich (10.1016/j.dam.2025.03.029_b3) 2016; 205 Marx (10.1016/j.dam.2025.03.029_b35) 2009; 157 Edmonds (10.1016/j.dam.2025.03.029_b19) 1965; 69B Shanthakumari (10.1016/j.dam.2025.03.029_b46) 2018 Sun (10.1016/j.dam.2025.03.029_b48) 2023; 337 Cheng (10.1016/j.dam.2025.03.029_b14) 2022; 313 Wang (10.1016/j.dam.2025.03.029_b51) 2010; 19 Mitchem (10.1016/j.dam.2025.03.029_b37) 1997; 17 Nemhauser (10.1016/j.dam.2025.03.029_b40) 1991; 10 Borghini (10.1016/j.dam.2025.03.029_b8) 2020; 286 Petrosyan (10.1016/j.dam.2025.03.029_b44) 2014; 165 |
| References_xml | – year: 2021 ident: b16 article-title: Problemas en coloreos de aristas con vértices adyacentes distinguibles – volume: 10 start-page: 315 year: 1991 end-page: 322 ident: b40 article-title: A polyhedral approach to edge coloring publication-title: Oper. Res. Lett. – volume: 109 start-page: 599 year: 2009 end-page: 602 ident: b13 article-title: Adjacent vertex-distinguishing edge and total chromatic numbers of hypercubes publication-title: Inform. Process. Lett. – reference: Aric A. Hagberg, Daniel A. Schult, Pieter J. Swart, Exploring Network Structure, Dynamics, and Function using NetworkX, in: Gaël Varoquaux, Travis Vaught, Jarrod Millman (Eds.), Proceedings of the 7th Python in Science Conference, Pasadena, CA USA, 2008, pp. 11–15. – volume: 158 start-page: 1216 year: 2010 end-page: 1223 ident: b11 article-title: Minimum sum edge colorings of multicycles publication-title: Discrete Appl. Math. – volume: 286 start-page: 11 year: 2020 end-page: 31 ident: b8 article-title: An exact algorithm for the edge coloring by total labeling problem publication-title: Ann. Oper. Res. – volume: 306 start-page: 3005 year: 2006 end-page: 3010 ident: b2 article-title: R-strong edge colorings of graphs publication-title: Discrete Math. – volume: 43 start-page: 710 year: 2022 end-page: 726 ident: b34 article-title: Adjacent vertex distinguishing edge coloring of IC-planar graphs publication-title: J. Comb. Optim. – volume: 75 start-page: 288 year: 1999 end-page: 301 ident: b6 article-title: On the vertex-distinguishing proper edge-colorings of graphs publication-title: J. Combin. Theory Ser. B – volume: 75 start-page: 65 year: 2000 end-page: 69 ident: b22 article-title: Edge-chromatic sum of trees and bounded cyclicity graphs publication-title: Inform. Process. Lett. – volume: 7 start-page: 67 year: 1982 end-page: 80 ident: b43 article-title: Odd minimum cut-sets and b-matchings publication-title: Math. Oper. Res. – volume: 11 year: 2023 ident: b23 article-title: Adjacent vertex distinguishing coloring of fuzzy graphs publication-title: Mathematics – start-page: 29 year: 1990 end-page: 36 ident: b1 article-title: Irregular assignments and two problems à la ringel publication-title: Topics in Combinatorics and Graph Theory – volume: 185 start-page: 220 year: 2015 end-page: 226 ident: b49 article-title: Adjacent vertex distinguishing edge-colorings and total-colorings of the lexicographic product of graphs publication-title: Discrete Appl. Math. – volume: 8 start-page: 97 year: 2004 end-page: 108 ident: b55 article-title: Algorithm for the cost edge-coloring of trees publication-title: J. Comb. Optim. – volume: 303 start-page: 39 year: 2021 end-page: 56 ident: b18 article-title: A branch-and-price algorithm for the minimum sum coloring problem publication-title: Discrete Appl. Math. – volume: 95 start-page: 246 year: 2005 end-page: 256 ident: b25 article-title: + 300 is a bound on the adjacent vertex distinguishing edge chromatic number publication-title: J. Combin. Theory Ser. B – volume: 22 start-page: 341 year: 2006 end-page: 350 ident: b20 article-title: On the neighbour-distinguishing index of a graph publication-title: Graphs Combin. – volume: 343 year: 2020 ident: b12 article-title: Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 8 publication-title: Discrete Math. – volume: 21 start-page: 237 year: 2007 end-page: 250 ident: b5 article-title: Adjacent vertex distinguishing edge-colorings publication-title: SIAM J. Discrete Math. – volume: 205 start-page: 1 year: 2016 end-page: 7 ident: b3 article-title: A note on adjacent vertex distinguishing colorings of graphs publication-title: Discrete Appl. Math. – year: 1996 ident: b27 article-title: Cliques, coloring, and satisfiability: Second DIMACS implementation challenge – start-page: 39 year: 1989 end-page: 45 ident: b31 article-title: An introduction to chromatic sums publication-title: Proceedings of the 17th Conference on ACM Annual Computer Science Conference – volume: 13 year: 2021 ident: b39 article-title: AVD proper edge-coloring of some families of graphs publication-title: International Journal of Mathematics for Industry – start-page: 288 year: 2001 end-page: 297 ident: b54 article-title: Algorithm for the cost edge-coloring of trees publication-title: Computing and Combinatorics: 7th Annual International Conference, COCOON 2001 Guilin, China, August 20–23, 2001 Proceedings 7 – volume: 3 start-page: 25 year: 1964 end-page: 30 ident: b50 article-title: On an estimate of the chromatic class of a p-graph publication-title: Diskretn. Anal. Issled. Oper. – volume: 165 start-page: 263 year: 2014 end-page: 269 ident: b44 article-title: On sum edge-coloring of regular,bipartite and split graphs publication-title: Discrete Appl. Math. – start-page: 15 year: 2007 end-page: 29 ident: b36 article-title: A branch-and-price approach for graph multi-coloring publication-title: Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies – volume: 3 start-page: 27 year: 2021 end-page: 42 ident: b38 article-title: AVD proper edge-coloring of some cycle related graphs publication-title: Ikonion Journal of Mathematics – volume: 159 start-page: 103 year: 1996 end-page: 109 ident: b21 article-title: Strong edge colorings of graphs publication-title: Discrete Math. – volume: 24 start-page: 2034 year: 2011 end-page: 2037 ident: b52 article-title: Adjacent vertex-distinguishing edge colorings of publication-title: Appl. Math. Lett. – volume: 69B start-page: 125 year: 1965 end-page: 130 ident: b19 article-title: Maximum matching and a polyhedron with 0, 1-vertices publication-title: Journal of Research of the National Bureau of Standards B – volume: 127 start-page: 477 year: 2003 end-page: 488 ident: b45 article-title: On sum coloring of graphs publication-title: Discrete Appl. Math. – volume: 14 start-page: 744 year: 1985 end-page: 780 ident: b15 article-title: Scheduling file transfers publication-title: SIAM J. Comput. – volume: 62 start-page: 273 year: 2017 end-page: 278 ident: b41 article-title: AVD-edge coloring on powers of paths publication-title: Electron. Notes Discrete Math. – volume: 337 start-page: 257 year: 2023 end-page: 271 ident: b48 article-title: Adjacent vertex distinguishing edge choosability of 1-planar graphs with maximum degree at least 23 publication-title: Discrete Appl. Math. – volume: 19 start-page: 471 year: 2010 end-page: 485 ident: b51 article-title: Adjacent vertex distinguishing edge-colorings of graphs with smaller maximum average degree publication-title: J. Comb. Optim. – volume: 236 start-page: 37 year: 2001 end-page: 42 ident: b7 article-title: A note on the vertex-distinguishing proper coloring of graphs with large minimum degree publication-title: Discrete Math. – volume: 2004 start-page: 1563 year: 2004 end-page: 1573 ident: b30 article-title: The chromatic sum of a graph: History and recent developments publication-title: Int. J. Math. Math. Sci. – volume: 3064 start-page: 196 year: 2004 end-page: 205 ident: b33 article-title: A faster exact separation algorithm for blossom inequalities – volume: 15 start-page: 623 year: 2002 end-page: 626 ident: b53 article-title: Adjacent strong edge coloring of graphs publication-title: Appl. Math. Lett. – volume: 34 start-page: 2221 year: 2020 end-page: 2238 ident: b28 article-title: Progress on the adjacent vertex distinguishing edge coloring conjecture publication-title: SIAM J. Discrete Math. – year: 2021 ident: b47 article-title: AVD chromatic index of publication-title: Adv. Appl. Math. Sci. – year: 2018 ident: b46 article-title: Adjacent vertex distinguishing chromatic index of certain nano structures publication-title: Int. J. Pure Appl. Math. – volume: 17 start-page: 229 year: 1997 end-page: 241 ident: b37 article-title: On the cost chromatic number of outerplanar, planar, and line graphs publication-title: Discuss. Math. Graph Theory – volume: 7 start-page: 67 year: 1982 end-page: 80 ident: b42 article-title: Odd minimum cut-sets and b-matchings publication-title: Math. Oper. Res. – volume: 31 year: 2011 ident: b9 article-title: Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six publication-title: Discuss. Math. Graph Theory – volume: 26 start-page: 73 year: 1997 end-page: 82 ident: b10 article-title: Vertex-distinguishing proper edge-colorings publication-title: J. Graph Theory – volume: 342 start-page: 1392 year: 2019 end-page: 1402 ident: b26 article-title: Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 9 publication-title: Discrete Math. – volume: 252 start-page: 17 year: 2002 end-page: 29 ident: b4 article-title: Vertex distinguishing colorings of graphs with publication-title: Discrete Math. – volume: 313 start-page: 29 year: 2022 end-page: 39 ident: b14 article-title: The adjacent vertex distinguishing edge choosability of planar graphs with maximum degree at least 11 publication-title: Discrete Appl. Math. – volume: 32 start-page: 43 year: 2019 end-page: 62 ident: b29 article-title: An integer programming approach to b-coloring publication-title: Discrete Optim. – volume: 13 start-page: 215 year: 1993 end-page: 223 ident: b32 article-title: A comparison of two edge-coloring formulations publication-title: Oper. Res. Lett. – volume: 218 start-page: 82 year: 2017 end-page: 97 ident: b17 article-title: On the algorithmic complexity of adjacent vertex closed distinguishing colorings number of graphs publication-title: Discrete Appl. Math. – volume: 157 start-page: 1034 year: 2009 end-page: 1045 ident: b35 article-title: Complexity results for minimum sum edge coloring publication-title: Discrete Appl. Math. – volume: 21 start-page: 237 issue: 1 year: 2007 ident: 10.1016/j.dam.2025.03.029_b5 article-title: Adjacent vertex distinguishing edge-colorings publication-title: SIAM J. Discrete Math. doi: 10.1137/S0895480102414107 – volume: 22 start-page: 341 issue: 3 year: 2006 ident: 10.1016/j.dam.2025.03.029_b20 article-title: On the neighbour-distinguishing index of a graph publication-title: Graphs Combin. doi: 10.1007/s00373-006-0671-2 – volume: 185 start-page: 220 year: 2015 ident: 10.1016/j.dam.2025.03.029_b49 article-title: Adjacent vertex distinguishing edge-colorings and total-colorings of the lexicographic product of graphs publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2014.11.028 – volume: 2004 start-page: 1563 issue: 30 year: 2004 ident: 10.1016/j.dam.2025.03.029_b30 article-title: The chromatic sum of a graph: History and recent developments publication-title: Int. J. Math. Math. Sci. doi: 10.1155/S0161171204306216 – volume: 127 start-page: 477 year: 2003 ident: 10.1016/j.dam.2025.03.029_b45 article-title: On sum coloring of graphs publication-title: Discrete Appl. Math. doi: 10.1016/S0166-218X(02)00249-4 – start-page: 29 year: 1990 ident: 10.1016/j.dam.2025.03.029_b1 article-title: Irregular assignments and two problems à la ringel – volume: 7 start-page: 67 issue: 1 year: 1982 ident: 10.1016/j.dam.2025.03.029_b42 article-title: Odd minimum cut-sets and b-matchings publication-title: Math. Oper. Res. doi: 10.1287/moor.7.1.67 – volume: 14 start-page: 744 issue: 3 year: 1985 ident: 10.1016/j.dam.2025.03.029_b15 article-title: Scheduling file transfers publication-title: SIAM J. Comput. doi: 10.1137/0214054 – year: 2021 ident: 10.1016/j.dam.2025.03.029_b47 article-title: AVD chromatic index of C5 C7 [p,q] and C5 C6 C7 [p,q] nanotubes publication-title: Adv. Appl. Math. Sci. – volume: 343 issue: 10 year: 2020 ident: 10.1016/j.dam.2025.03.029_b12 article-title: Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 8 publication-title: Discrete Math. doi: 10.1016/j.disc.2020.112014 – volume: 3064 start-page: 196 year: 2004 ident: 10.1016/j.dam.2025.03.029_b33 article-title: A faster exact separation algorithm for blossom inequalities – ident: 10.1016/j.dam.2025.03.029_b24 doi: 10.25080/TCWV9851 – year: 1996 ident: 10.1016/j.dam.2025.03.029_b27 – volume: 236 start-page: 37 issue: 1 year: 2001 ident: 10.1016/j.dam.2025.03.029_b7 article-title: A note on the vertex-distinguishing proper coloring of graphs with large minimum degree publication-title: Discrete Math. doi: 10.1016/S0012-365X(00)00428-3 – volume: 205 start-page: 1 year: 2016 ident: 10.1016/j.dam.2025.03.029_b3 article-title: A note on adjacent vertex distinguishing colorings of graphs publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2015.12.005 – volume: 95 start-page: 246 issue: 2 year: 2005 ident: 10.1016/j.dam.2025.03.029_b25 article-title: Δ+ 300 is a bound on the adjacent vertex distinguishing edge chromatic number publication-title: J. Combin. Theory Ser. B doi: 10.1016/j.jctb.2005.04.002 – volume: 43 start-page: 710 year: 2022 ident: 10.1016/j.dam.2025.03.029_b34 article-title: Adjacent vertex distinguishing edge coloring of IC-planar graphs publication-title: J. Comb. Optim. doi: 10.1007/s10878-021-00807-0 – volume: 13 start-page: 215 issue: 4 year: 1993 ident: 10.1016/j.dam.2025.03.029_b32 article-title: A comparison of two edge-coloring formulations publication-title: Oper. Res. Lett. doi: 10.1016/0167-6377(93)90043-G – volume: 303 start-page: 39 year: 2021 ident: 10.1016/j.dam.2025.03.029_b18 article-title: A branch-and-price algorithm for the minimum sum coloring problem publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2020.08.031 – volume: 3 start-page: 27 issue: 2 year: 2021 ident: 10.1016/j.dam.2025.03.029_b38 article-title: AVD proper edge-coloring of some cycle related graphs publication-title: Ikonion Journal of Mathematics doi: 10.54286/ikjm.972238 – volume: 24 start-page: 2034 issue: 12 year: 2011 ident: 10.1016/j.dam.2025.03.029_b52 article-title: Adjacent vertex-distinguishing edge colorings of K4-minor free graphs publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2011.05.038 – volume: 286 start-page: 11 year: 2020 ident: 10.1016/j.dam.2025.03.029_b8 article-title: An exact algorithm for the edge coloring by total labeling problem publication-title: Ann. Oper. Res. doi: 10.1007/s10479-018-2977-x – volume: 69B start-page: 125 year: 1965 ident: 10.1016/j.dam.2025.03.029_b19 article-title: Maximum matching and a polyhedron with 0, 1-vertices publication-title: Journal of Research of the National Bureau of Standards B doi: 10.6028/jres.069B.013 – volume: 62 start-page: 273 year: 2017 ident: 10.1016/j.dam.2025.03.029_b41 article-title: AVD-edge coloring on powers of paths publication-title: Electron. Notes Discrete Math. doi: 10.1016/j.endm.2017.10.047 – volume: 34 start-page: 2221 issue: 4 year: 2020 ident: 10.1016/j.dam.2025.03.029_b28 article-title: Progress on the adjacent vertex distinguishing edge coloring conjecture publication-title: SIAM J. Discrete Math. doi: 10.1137/18M1200427 – volume: 337 start-page: 257 year: 2023 ident: 10.1016/j.dam.2025.03.029_b48 article-title: Adjacent vertex distinguishing edge choosability of 1-planar graphs with maximum degree at least 23 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2023.05.010 – volume: 109 start-page: 599 issue: 12 year: 2009 ident: 10.1016/j.dam.2025.03.029_b13 article-title: Adjacent vertex-distinguishing edge and total chromatic numbers of hypercubes publication-title: Inform. Process. Lett. doi: 10.1016/j.ipl.2009.02.006 – volume: 306 start-page: 3005 year: 2006 ident: 10.1016/j.dam.2025.03.029_b2 article-title: R-strong edge colorings of graphs publication-title: Discrete Math. doi: 10.1016/j.disc.2004.12.027 – volume: 31 issue: 3 year: 2011 ident: 10.1016/j.dam.2025.03.029_b9 article-title: Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six publication-title: Discuss. Math. Graph Theory doi: 10.7151/dmgt.1556 – volume: 75 start-page: 288 issue: 2 year: 1999 ident: 10.1016/j.dam.2025.03.029_b6 article-title: On the vertex-distinguishing proper edge-colorings of graphs publication-title: J. Combin. Theory Ser. B doi: 10.1006/jctb.1998.1884 – volume: 7 start-page: 67 issue: 1 year: 1982 ident: 10.1016/j.dam.2025.03.029_b43 article-title: Odd minimum cut-sets and b-matchings publication-title: Math. Oper. Res. doi: 10.1287/moor.7.1.67 – volume: 159 start-page: 103 issue: 1 year: 1996 ident: 10.1016/j.dam.2025.03.029_b21 article-title: Strong edge colorings of graphs publication-title: Discrete Math. doi: 10.1016/0012-365X(95)00102-3 – volume: 157 start-page: 1034 issue: 5 year: 2009 ident: 10.1016/j.dam.2025.03.029_b35 article-title: Complexity results for minimum sum edge coloring publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2008.04.002 – volume: 10 start-page: 315 issue: 6 year: 1991 ident: 10.1016/j.dam.2025.03.029_b40 article-title: A polyhedral approach to edge coloring publication-title: Oper. Res. Lett. doi: 10.1016/0167-6377(91)90003-8 – year: 2018 ident: 10.1016/j.dam.2025.03.029_b46 article-title: Adjacent vertex distinguishing chromatic index of certain nano structures publication-title: Int. J. Pure Appl. Math. – volume: 13 issue: 01 year: 2021 ident: 10.1016/j.dam.2025.03.029_b39 article-title: AVD proper edge-coloring of some families of graphs publication-title: International Journal of Mathematics for Industry doi: 10.1142/S2661335222500010 – volume: 3 start-page: 25 issue: 7 year: 1964 ident: 10.1016/j.dam.2025.03.029_b50 article-title: On an estimate of the chromatic class of a p-graph publication-title: Diskretn. Anal. Issled. Oper. – volume: 252 start-page: 17 issue: 1 year: 2002 ident: 10.1016/j.dam.2025.03.029_b4 article-title: Vertex distinguishing colorings of graphs with δ(G)=2 publication-title: Discrete Math. doi: 10.1016/S0012-365X(01)00287-4 – volume: 32 start-page: 43 issn: 1572-5286 year: 2019 ident: 10.1016/j.dam.2025.03.029_b29 article-title: An integer programming approach to b-coloring publication-title: Discrete Optim. doi: 10.1016/j.disopt.2018.12.001 – start-page: 15 year: 2007 ident: 10.1016/j.dam.2025.03.029_b36 article-title: A branch-and-price approach for graph multi-coloring – start-page: 288 year: 2001 ident: 10.1016/j.dam.2025.03.029_b54 article-title: Algorithm for the cost edge-coloring of trees – volume: 26 start-page: 73 issue: 2 year: 1997 ident: 10.1016/j.dam.2025.03.029_b10 article-title: Vertex-distinguishing proper edge-colorings publication-title: J. Graph Theory doi: 10.1002/(SICI)1097-0118(199710)26:2<73::AID-JGT2>3.0.CO;2-C – volume: 218 start-page: 82 year: 2017 ident: 10.1016/j.dam.2025.03.029_b17 article-title: On the algorithmic complexity of adjacent vertex closed distinguishing colorings number of graphs publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2016.10.028 – volume: 17 start-page: 229 issue: 2 year: 1997 ident: 10.1016/j.dam.2025.03.029_b37 article-title: On the cost chromatic number of outerplanar, planar, and line graphs publication-title: Discuss. Math. Graph Theory doi: 10.7151/dmgt.1050 – volume: 19 start-page: 471 issue: 4 year: 2010 ident: 10.1016/j.dam.2025.03.029_b51 article-title: Adjacent vertex distinguishing edge-colorings of graphs with smaller maximum average degree publication-title: J. Comb. Optim. doi: 10.1007/s10878-008-9178-5 – volume: 313 start-page: 29 year: 2022 ident: 10.1016/j.dam.2025.03.029_b14 article-title: The adjacent vertex distinguishing edge choosability of planar graphs with maximum degree at least 11 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2022.01.003 – volume: 8 start-page: 97 year: 2004 ident: 10.1016/j.dam.2025.03.029_b55 article-title: Algorithm for the cost edge-coloring of trees publication-title: J. Comb. Optim. doi: 10.1023/B:JOCO.0000021940.40066.0c – volume: 158 start-page: 1216 issue: 12 year: 2010 ident: 10.1016/j.dam.2025.03.029_b11 article-title: Minimum sum edge colorings of multicycles publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2009.04.020 – volume: 342 start-page: 1392 issue: 5 year: 2019 ident: 10.1016/j.dam.2025.03.029_b26 article-title: Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 9 publication-title: Discrete Math. doi: 10.1016/j.disc.2019.01.024 – volume: 75 start-page: 65 issue: 1–2 year: 2000 ident: 10.1016/j.dam.2025.03.029_b22 article-title: Edge-chromatic sum of trees and bounded cyclicity graphs publication-title: Inform. Process. Lett. doi: 10.1016/S0020-0190(00)00072-7 – year: 2021 ident: 10.1016/j.dam.2025.03.029_b16 – volume: 11 issn: 2227-7390 issue: 10 year: 2023 ident: 10.1016/j.dam.2025.03.029_b23 article-title: Adjacent vertex distinguishing coloring of fuzzy graphs publication-title: Mathematics doi: 10.3390/math11102233 – start-page: 39 year: 1989 ident: 10.1016/j.dam.2025.03.029_b31 article-title: An introduction to chromatic sums – volume: 165 start-page: 263 year: 2014 ident: 10.1016/j.dam.2025.03.029_b44 article-title: On sum edge-coloring of regular,bipartite and split graphs publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2013.09.025 – volume: 15 start-page: 623 issue: 5 year: 2002 ident: 10.1016/j.dam.2025.03.029_b53 article-title: Adjacent strong edge coloring of graphs publication-title: Appl. Math. Lett. doi: 10.1016/S0893-9659(02)80015-5 |
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| Title | An exact algorithm for the adjacent vertex distinguishing sum edge coloring problem |
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