TY - GEN

T1 - The perfect matching reconfiguration problem

AU - Bonamy, Marthe

AU - Bousquet, Nicolas

AU - Heinrich, Marc

AU - Ito, Takehiro

AU - Kobayashi, Yusuke

AU - Mary, Arnaud

AU - Mühlenthaler, Moritz

AU - Wasa, Kunihiro

N1 - Funding Information:
Acknowledgements This work is partially supported by JSPS and MAEDI under the Japan-France Integrated Action Program (SAKURA).
Funding Information:
Funding Marthe Bonamy: Partially supported by ANR project GrR (ANR-18-CE40-0032). Nicolas Bousquet: Partially supported by ANR project GrR (ANR-18-CE40-0032). Marc Heinrich: Partially supported by ANR project GrR (ANR-18-CE40-0032). Takehiro Ito: Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP18H04091 and JP19K11814, Japan. Yusuke Kobayashi: Supported by JST ACT-I Grant Number JPMJPR17UB, and JSPS KAKENHI Grant Numbers JP16K16010, JP16H03118, JP17K19960 and JP18H05291, Japan. Arnaud Mary: Partially supported by ANR project GrR (ANR-18-CE40-0032). Kunihiro Wasa: Partially supported by JST CREST Grant Number JPMJCR1401 and JPMJCR18K3, and JSPS KAKENHI Grant Number JP19K20350, Japan.
Publisher Copyright:
© Marthe Bonamy, Nicolas Bousquet, Marc Heinrich, Takehiro Ito, Yusuke Kobayashi, Arnaud Mary, Moritz Mühlenthaler, and Kunihiro Wasa.

PY - 2019/8

Y1 - 2019/8

N2 - 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.

AB - 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.

KW - Combinatorial Reconfiguration

KW - Graph Algorithms

KW - Perfect Matching

UR - http://www.scopus.com/inward/record.url?scp=85071773570&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071773570&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.MFCS.2019.80

DO - 10.4230/LIPIcs.MFCS.2019.80

M3 - Conference contribution

AN - SCOPUS:85071773570

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019

A2 - Katoen, Joost-Pieter

A2 - Heggernes, Pinar

A2 - Rossmanith, Peter

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019

Y2 - 26 August 2019 through 30 August 2019

ER -