TY - JOUR
T1 - The coloring reconfiguration problem on specific graph classes
AU - Hatanaka, Tatsuhiko
AU - Ito, Takehiro
AU - Zhou, Xiao
N1 - Funding Information:
Manuscript received March 20, 2018. Manuscript revised June 4, 2018. Manuscript publicized October 30, 2018. †The authors are with Graduate School of Information Sciences, Tohoku University, Sendai-shi, 980–8579 Japan. ∗A preliminary version of this paper has been presented at the 11th Annual International Conference on Combinatorial Optimization and Applications (COCOA 2017) [11]. This work is partially supported by JST CREST Grant Number JPMJCR1402, and by JSPS KAKENHI Grant Numbers JP16J02175, JP16K00003, and JP16K00004, Japan. a) E-mail: hatanaka@ecei.tohoku.ac.jp b) E-mail: takehiro@ecei.tohoku.ac.jp c) E-mail: zhou@ecei.tohoku.ac.jp DOI: 10.1587/transinf.2018FCP0005
Publisher Copyright:
Copyright © 2019 The Institute of Electronics, Information and Communication Engineers.
PY - 2019/3/1
Y1 - 2019/3/1
N2 - We study the problem of transforming one (vertex) ccoloring of a graph into another one by changing only one vertex color assignment at a time, while at all times maintaining a c-coloring, where c denotes the number of colors. This decision problem is known to be PSPACE-complete even for bipartite graphs and any fixed constant c ≥ 4. In this paper, we study the problem from the viewpoint of graph classes. We first show that the problem remains PSPACE-complete for chordal graphs even if c is a fixed constant. We then demonstrate that, even when c is a part of input, the problem is solvable in polynomial time for several graph classes, such as k-trees with any integer k ≥ 1, split graphs, and trivially perfect graphs.
AB - We study the problem of transforming one (vertex) ccoloring of a graph into another one by changing only one vertex color assignment at a time, while at all times maintaining a c-coloring, where c denotes the number of colors. This decision problem is known to be PSPACE-complete even for bipartite graphs and any fixed constant c ≥ 4. In this paper, we study the problem from the viewpoint of graph classes. We first show that the problem remains PSPACE-complete for chordal graphs even if c is a fixed constant. We then demonstrate that, even when c is a part of input, the problem is solvable in polynomial time for several graph classes, such as k-trees with any integer k ≥ 1, split graphs, and trivially perfect graphs.
KW - Chordal graphs
KW - Combinatorial reconfiguration
KW - Graph algorithm
KW - Graph coloring
KW - PSPACE-complete
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U2 - 10.1587/transinf.2018FCP0005
DO - 10.1587/transinf.2018FCP0005
M3 - Article
AN - SCOPUS:85063988572
VL - E102D
SP - 423
EP - 429
JO - IEICE Transactions on Information and Systems
JF - IEICE Transactions on Information and Systems
SN - 0916-8532
IS - 3
ER -