Decremental optimization of vertex-colouring under the reconfiguration framework
Suppose that we are given a positive integer k, and a k-(vertex-)colouring of a given graph G. Then we are asked to find a colouring of G using the minimum number of colours among colourings that are reachable from by iteratively changing a colour assignment of exactly one vertex while maintaining t...
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| Published in: | International journal of computer mathematics. Computer systems theory Vol. 8; no. 1; pp. 80 - 92 |
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| Main Authors: | , , , |
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Taylor & Francis
02.01.2023
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| ISSN: | 2379-9927, 2379-9935 |
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| Abstract | Suppose that we are given a positive integer k, and a k-(vertex-)colouring
of a given graph G. Then we are asked to find a colouring of G using the minimum number of colours among colourings that are reachable from
by iteratively changing a colour assignment of exactly one vertex while maintaining the property of k-colourings. In this paper, we give linear-time algorithms to solve the problem for graphs of degeneracy at most two and for the case where
. These results imply linear-time algorithms for series-parallel graphs and grid graphs. In addition, we give linear-time algorithms for chordal graphs and cographs. On the other hand, we show that, for any
, this problem remains NP-hard for planar graphs with degeneracy three and maximum degree four. Thus, we obtain a complexity dichotomy for this problem with respect to the degeneracy of a graph and the number k of colours. |
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| AbstractList | Suppose that we are given a positive integer k, and a k-(vertex-)colouring
of a given graph G. Then we are asked to find a colouring of G using the minimum number of colours among colourings that are reachable from
by iteratively changing a colour assignment of exactly one vertex while maintaining the property of k-colourings. In this paper, we give linear-time algorithms to solve the problem for graphs of degeneracy at most two and for the case where
. These results imply linear-time algorithms for series-parallel graphs and grid graphs. In addition, we give linear-time algorithms for chordal graphs and cographs. On the other hand, we show that, for any
, this problem remains NP-hard for planar graphs with degeneracy three and maximum degree four. Thus, we obtain a complexity dichotomy for this problem with respect to the degeneracy of a graph and the number k of colours. |
| Author | Tamura, Yuma Zhou, Xiao Suzuki, Akira Yanagisawa, Yusuke |
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| References | Bonsma P.S. (CIT0004) 2009; 410 Feghali C. (CIT0011) 2016; 83 Bonamy M. (CIT0003) 2014; 27 Ito T. (CIT0015) 2011; 412 Markossian S.E. (CIT0020) 1996; 67 Ito T. (CIT0017) 2020; 43 Cereceda L. (CIT0008) 2011; 67 CIT0010 Cereceda L. (CIT0007) 2008; 308 CIT0001 CIT0023 CIT0022 Garey M.R. (CIT0012) 1979 Wrochna M. (CIT0024) 2018; 93 Johnson M. (CIT0018) 2016; 75 Bonsma P.S. (CIT0006) 2019; 56 Hatanaka T. (CIT0013) 2019; 102 Mynhardt C.M. (CIT0021) 2019 CIT0014 CIT0005 CIT0016 Bonamy M. (CIT0002) 2018; 69 CIT0009 CIT0019 |
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| Snippet | Suppose that we are given a positive integer k, and a k-(vertex-)colouring
of a given graph G. Then we are asked to find a colouring of G using the minimum... |
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| SubjectTerms | Combinatorial reconfiguration graph algorithms graph colouring linear-time algorithms |
| Title | Decremental optimization of vertex-colouring under the reconfiguration framework |
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