Finding Matching Cuts in H-Free Graphs
The well-known NP-complete problem Matching Cut is to decide if a graph has a matching that is also an edge cut of the graph. We prove new complexity results for Matching Cut restricted to H-free graphs, that is, graphs that do not contain some fixed graph H as an induced subgraph. We also prove new complexity results for two recently studied variants of Matching Cut, on H-free graphs. The first variant requires that the matching cut must be extendable to a perfect matching of the graph. The second variant requires the matching cut to be a perfect matching. In particular, we prove that there exists a small constant r > 0 such that the first variant is NP-complete for P_r-free graphs. This addresses a question of Bouquet and Picouleau (arXiv, 2020). For all three problems, we give state-of-the-art summaries of their computational complexity for H-free graphs.
matching cut
perfect matching
H-free graph
computational complexity
Mathematics of computing~Graph algorithms
22:1-22:16
Regular Paper
Felicia
Lucke
Felicia Lucke
Department of Informatics, University of Fribourg, Switzerland
https://orcid.org/0000-0002-9860-2928
Daniël
Paulusma
Daniël Paulusma
Department of Computer Science, Durham University, UK
https://orcid.org/0000-0001-5945-9287
Bernard
Ries
Bernard Ries
Department of Informatics, University of Fribourg, Switzerland
https://orcid.org/0000-0003-4395-5547
10.4230/LIPIcs.ISAAC.2022.22
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Felicia Lucke, Daniël Paulusma, and Bernard Ries
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