On some graphs with a unique perfect matching

Steven Chaplick, Maximilian Fürst, Frédéric Maffray, Dieter Rautenbach*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Combining known results it follows that deciding whether a given graph G of size m has a unique perfect matching as well as finding that matching if it exists, can be done in time O(m) if G is either a cograph, or a split graph, or a claw-free graph. We provide structural insights concerning the graphs with a unique perfect matching that belong to these three graph classes, which lead to simple linear time algorithms for the unique perfect matching problem. (C) 2018 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)60-63
JournalInformation Processing Letters
Volume139
DOIs
Publication statusPublished - 2018
Externally publishedYes

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