Diameter of Colorings Under Kempe Changes

Marthe Bonamy, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Haruka Mizuta, Moritz Mühlenthaler, Akira Suzuki, Kunihiro Wasa

研究成果: Conference contribution

3 被引用数 (Scopus)

抄録

Given a k-coloring of a graph G, a Kempe-change for two colors a and b produces another k-coloring of G, as follows: first choose a connected component in the subgraph of G induced by the two color classes of a and b, and then swap the colors a and b in the component. Two k-colorings are called Kempe-equivalent if one can be transformed into the other by a sequence of Kempe-changes. We consider two problems, defined as follows: First, given two k-colorings of a graph G, Kempe Reachability asks whether they are Kempe-equivalent; and second, given a graph G and a positive integer k, Kempe Connectivity asks whether any two k-colorings of G are Kempe-equivalent. We analyze the complexity of these problems from the viewpoint of graph classes. We prove that Kempe Reachability is PSPACE-complete for any fixed k ≥, and that it remains PSPACE-complete even when restricted to three colors and planar graphs of maximum degree six. Furthermore, we show that both problems admit polynomial-time algorithms on chordal graphs, bipartite graphs, and cographs. For each of these graph classes, we give a non-trivial upper bound on the number of Kempe-changes needed in order to certify that two k-colorings are Kempe-equivalent.

本文言語English
ホスト出版物のタイトルComputing and Combinatorics - 25th International Conference, COCOON 2019, Proceedings
編集者Ding-Zhu Du, Zhenhua Duan, Cong Tian
出版社Springer Verlag
ページ52-64
ページ数13
ISBN(印刷版)9783030261757
DOI
出版ステータスPublished - 2019
イベント25th International Computing and Combinatorics Conference, COCOON 2019 - Xi'an, China
継続期間: 2019 7 292019 7 31

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
11653 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Conference

Conference25th International Computing and Combinatorics Conference, COCOON 2019
国/地域China
CityXi'an
Period19/7/2919/7/31

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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