The perfect matching reconfiguration problem

Marthe Bonamy, Nicolas Bousquet, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Arnaud Mary, Moritz Mühlenthaler, Kunihiro Wasa

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of length four. We are interested in the complexity of this decision problem from the viewpoint of graph classes. We first prove that the problem is PSPACE-complete even for split graphs and for bipartite graphs of bounded bandwidth with maximum degree five. We then investigate polynomial-time solvable cases. Specifically, we prove that the problem is solvable in polynomial time for strongly orderable graphs (that include interval graphs and strongly chordal graphs), for outerplanar graphs, and for cographs (also known as P4-free graphs). Furthermore, for each yes-instance from these graph classes, we show that a linear number of flip operations is sufficient and we can exhibit a corresponding sequence of flip operations in polynomial time.

本文言語English
ホスト出版物のタイトル44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019
編集者Joost-Pieter Katoen, Pinar Heggernes, Peter Rossmanith
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN(電子版)9783959771177
DOI
出版ステータスPublished - 2019 8
イベント44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019 - Aachen, Germany
継続期間: 2019 8 262019 8 30

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
138
ISSN(印刷版)1868-8969

Conference

Conference44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019
国/地域Germany
CityAachen
Period19/8/2619/8/30

ASJC Scopus subject areas

  • ソフトウェア

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