On the complexity of matching cut for graphs of bounded radius and H-free graphs
BP2-STS
- Lucke, Felicia ORCID Université de Fribourg, Switzerland
- Paulusma, Daniel ORCID Durham University, United Kingdom
- Ries, Bernard ORCID Université de Fribourg, Switzerland
- 21.09.2022
Published in:
- Theoretical Computer Science. - Elsevier BV. - 2022, vol. 936, p. 33-42
English
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 (sP3+P6)-free graphs for every s≥0 and initiate a complexity classification of Matching Cut for H-free graphs.
- Faculty
- Faculté des sciences économiques et sociales et du management
- Department
- Département d'informatique
- Language
-
- English
- Classification
- Computer science and technology
- License
- CC BY
- Open access status
- hybrid
- Identifiers
-
- DOI 10.1016/j.tcs.2022.09.014
- ISSN 0304-3975
- Persistent URL
- https://folia.unifr.ch/unifr/documents/325861
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