The complexity of the perfect matching‐cut problem - Archive ouverte HAL
Article Dans Une Revue Journal of Graph Theory Année : 2024

The complexity of the perfect matching‐cut problem

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Abstract PERFECT MATCHING‐CUT is the problem of deciding whether a graph has a perfect matching that contains 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, ‐free, diameter two, bipartite with diameter three, and graphs with bounded treewidth.
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hal-04723408 , version 1 (08-10-2024)

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Valentin Bouquet, Christophe Picouleau. The complexity of the perfect matching‐cut problem. Journal of Graph Theory, 2024, ⟨10.1002/jgt.23167⟩. ⟨hal-04723408⟩
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