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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| Vydáno v: | International journal of computer mathematics. Computer systems theory Ročník 8; číslo 1; s. 80 - 92 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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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 |
| Author_xml | – sequence: 1 givenname: Yusuke surname: Yanagisawa fullname: Yanagisawa, Yusuke email: yusuke.yanagisawa.r7@dc.tohoku.ac.jp organization: Tohoku University – sequence: 2 givenname: Akira surname: Suzuki fullname: Suzuki, Akira organization: Tohoku University – sequence: 3 givenname: Yuma surname: Tamura fullname: Tamura, Yuma organization: Tohoku University – sequence: 4 givenname: Xiao surname: Zhou fullname: Zhou, Xiao organization: Tohoku University |
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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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