Finding Matching Cuts in H-Free Graphs

Abstract The well-known -complete problem Matching Cut is to decide if a graph has matching that also an edge cut of the graph. We prove new complexity results for restricted H -free graphs, is, graphs do not contain some fixed as induced subgraph. two recently studied variants , on graphs. first variant requires must be extendable perfect second matching. In particular, we there exists small constant $$r>0$$ r > 0 such $$P_r$$ P This addresses question Bouquet and Picouleau (The Perfect Matching-Cut problem. CoRR, arXiv:2011.03318 (2020)). For all three problems, give state-of-the-art summaries their computational