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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| Vydané v: | International journal of computer mathematics. Computer systems theory Ročník 8; číslo 1; s. 80 - 92 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Taylor & Francis
02.01.2023
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| Predmet: | |
| ISSN: | 2379-9927, 2379-9935 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | 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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| ISSN: | 2379-9927 2379-9935 |
| DOI: | 10.1080/23799927.2023.2185543 |