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 n...

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Bibliographic Details
Published in:Algorithmica 2023-10, Vol.85 (10), p.3290-3322
Main Authors: Lucke, Felicia, Paulusma, Daniël, Ries, Bernard
Format: Article
Language:English
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Complexity
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graph theory
Graphs
Matching
Mathematics of Computing
Theory of Computation
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Summary: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 (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.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-023-01137-9