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arXiv · 1504.02250

Graphs in which some and every maximum matching is uniquely restricted

Lucia Draque Penso·Dieter Rautenbach·Ueverton dos Santos Souza
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Abstract

A matching $M$ in a graph $G$ is uniquely restricted if there is no matching $M'$ in $G$ that is distinct from $M$ but covers the same vertices as $M$. Solving a problem posed by Golumbic, Hirst, and Lewenstein, we characterize the graphs in which some maximum matching is uniquely restricted. Solving a problem posed by Levit and Mandrescu, we characterize the graphs in which every maximum matching is uniquely restricted. Both our characterizations lead to efficient recognition algorithms for the corresponding graphs.

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Lucia Draque Penso, Dieter Rautenbach, Ueverton dos Santos Souza. 2015-04-09. Graphs in which some and every maximum matching is uniquely restricted. https://arxiv.org/abs/1504.02250

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