Finding matching cuts in \(H\)-free graphs
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Publication:6046951
DOI10.1007/S00453-023-01137-9arXiv2207.07095OpenAlexW4379796487MaRDI QIDQ6046951
Author name not available (Why is that?)
Publication date: 6 October 2023
Published in: (Search for Journal in Brave)
Abstract: The 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 -free graphs, that is, graphs that do not contain some fixed graph as an induced subgraph. We also prove new complexity results for two recently studied variants of Matching Cut, on -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 such that the first variant is NP-complete for -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 -free graphs.
Full work available at URL: https://arxiv.org/abs/2207.07095
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