Lucke, Felicia Paulusma, Daniël Ries, Bernard 2022-12-14 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 Pr-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. application/pdf https://folia.unifr.ch/global/documents/322855 https://folia.unifr.ch/documents/322855/files/lipics-isaac-2022-22.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.4230/LIPIcs.ISAAC.2022.22 info:eu-repo/semantics/openAccess CC BY 33rd International Symposium on Algorithms and Computation (ISAAC 2022). - Schloss Dagstuhl - Leibniz-Zentrum für Informatik. - 2022, p. 22:1-22:16 Matching cut Perfect matching H-free graph Computational complexity info:eu-repo/classification/udc/004 Finding Matching Cuts in H-Free Graphs http://purl.org/coar/resource_type/c_5794