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Preprints, Working Papers, ... Year : 2020

The complexity of the Perfect Matching-Cut problem

Abstract

Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that is an edge cut. We show that this problem is $NP$-complete for planar graphs with maximum degree four, for planar graphs with girth five, for bipartite five-regular graphs, for graphs of diameter three and for bipartite graphs of diameter four. We show that there exist polynomial time algorithms for the following classes of graphs: claw-free, $P_5$-free, diameter two, bipartite with diameter three, quadrangulated and graphs with bounded tree-width.

Dates and versions

hal-02995237 , version 1 (09-11-2020)

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Valentin Bouquet, Christophe Picouleau. The complexity of the Perfect Matching-Cut problem. 2020. ⟨hal-02995237⟩
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