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
Journal	Information Processing Letters
Volume	139
DOIs	https://doi.org/10.1016/J.IPL.2018.07.008
Publication status	Published - 2018
Externally published	Yes

Access to Document

10.1016/J.IPL.2018.07.008

Cite this

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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 - Fürst, Maximilian

AU - Maffray, Frédéric

AU - Rautenbach, Dieter

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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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