Dichotomies for Maximum Matching Cut: H-freeness, bounded diameter, bounded radius
Year: 2024
Type: article
Abstract: Matching cut Perfect matching π»-free graph Diameter Radius DichotomyThe (Perfect) Matching Cut problem is to decide if a graph πΊ has a (perfect) matching cut, i.e., a (perfect) matching that is also an edge cut of πΊ.Both Matching Cut and Perfect Matching Cut are known to be NP-complete.A perfect matching cut is also a matching cut with maximum number of edges.To increase our understanding of the relationship between the two problems, we perform a complexity study for the Maximum Matching Cut problem, which is to determine a largest matching cut in a graph.Our results yield full dichotomies of Maximum Matching Cut for graphs of bounded diameter, bounded radius and π»-free graphs.A disconnected perfect matching of a graph πΊ is a perfect matching that contains a matching cut of πΊ.We also show how our new techniques can be used for finding a disconnected perfect matching with a largest matching cut for special graph classes.In this way we can prove that the decision problem Disconnected Perfect Matching is polynomial-time solvable for (π 6 + π π 2 )-free graphs for every π β₯ 0, extending a known result for π 5 -free graphs (Bouquet and Picouleau, 2020).
Source: Theoretical Computer Science
Authors: Felicia Lucke, DaniΓ«l Paulusma, Bernard Ries
Institutions: University of Fribourg, Durham University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,800
OpenAlex ID: W4401741726