On the complexity of matching cut for graphs of bounded radius and H-free graphs

Lucke, F.; Paulusma, D.; Ries, B.

Abstract

For a connected graph G = (V , E), a matching M ⊆ E is a matching cut of G if G − M is disconnected. It is known that for an integer d, the corresponding decision problem Matching Cut is polynomial-time solvable for graphs of diameter at most d if d ≤ 2 and NP-complete if d ≥ 3. We prove the same dichotomy for graphs of bounded radius. For a graph H, a graph is H-free if it does not contain H as an induced subgraph. As a consequence of our result, we can solve Matching Cut in polynomial time for P6- free graphs, extending a recent result of Feghali for P5-free graphs. We then extend our result to hold even for (s P3 + P6)-free graphs for every s ≥ 0 and initiate a complexity classification of Matching Cut for H-free graphs.

Citation

Lucke, F., Paulusma, D., & Ries, B. (2022). On the complexity of matching cut for graphs of bounded radius and H-free graphs. Theoretical Computer Science, 936, 33-42. https://doi.org/10.1016/j.tcs.2022.09.014

• Journal Article Type: Article
• Acceptance Date: Sep 15, 2022
• Online Publication Date: Sep 21, 2022
• Publication Date: 2022
• Deposit Date: Oct 16, 2022
• Publicly Available Date: Oct 17, 2022
• Journal: Theoretical Computer Science
• Print ISSN: 0304-3975
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 936
• Pages: 33-42
• DOI: https://doi.org/10.1016/j.tcs.2022.09.014
• Public URL: https://durham-repository.worktribe.com/output/1188716