On some graphs with a unique perfect matching

Steven Chaplick; Maximilian Fürst; Frédéric Maffray; Dieter Rautenbach

doi:10.1016/J.IPL.2018.07.008

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 journal › Article › Academic › peer-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 language	English
Pages (from-to)	60-63
Number of pages	4
Journal	Information Processing Letters
Volume	139
DOIs	https://doi.org/10.1016/J.IPL.2018.07.008
Publication status	Published - 2018
Externally published	Yes

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10.1016/J.IPL.2018.07.008

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title = "On some graphs with a unique perfect matching",

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.",

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AU - Chaplick, Steven

AU - Fürst, Maximilian

AU - Maffray, Frédéric

AU - Rautenbach, Dieter

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

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M3 - Article

SN - 0020-0190

VL - 139

SP - 60

EP - 63

JO - Information Processing Letters

JF - Information Processing Letters

ER -

On some graphs with a unique perfect matching

Abstract

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