F. Lucke
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 |
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Copyright Statement
This is an open access article distributed under the terms of the Creative Commons CC-BY license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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