On some Graphs with a Unique Perfect Matching
Abstract
We show 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 an interval graph, or claw-free. Furthermore, we provide a constructive characterization of the claw-free graphs with a unique perfect matching.
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