Lucke, Felicia Paulusma, Daniël Ries, Bernard 2023 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 NPcomplete for Pr -free graphs. This addresses a question of Bouquet and Picouleau (The complexity of the Perfect Matching-Cut problem. CoRR, arXiv:2011.03318, (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/328989 https://folia.unifr.ch/documents/328989/files/mc_0.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00453-023-01137-9 info:eu-repo/semantics/altIdentifier/issn/0178-4617 info:eu-repo/semantics/openAccess CC BY Algorithmica. - Springer Science and Business Media LLC. - 2023, vol. 85, no. 10, p. 3290-3322 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_6501