# The complexity of the Perfect Matching-Cut problem

1 CEDRIC - OC - CEDRIC. Optimisation Combinatoire
CEDRIC - Centre d'études et de recherche en informatique et communications
2 CEDRIC - ROC - CEDRIC. Réseaux et Objets Connectés
CEDRIC - Centre d'études et de recherche en informatique et communications
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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-02995237
Contributor : Valentin Bouquet Connect in order to contact the contributor
Submitted on : Monday, November 9, 2020 - 9:39:02 AM
Last modification on : Thursday, December 3, 2020 - 2:09:42 PM

### Identifiers

• HAL Id : hal-02995237, version 1
• ARXIV : 2011.03318

### Citation

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

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