Work

The complexity of the perfect matching‐cut problem

Year: 2024

Type: article

Abstract: PERFECT MATCHING‐CUT is the problem of deciding whether a graph has a perfect matching that contains an edge‐cut. We show that this problem is NP‐complete for planar graphs with maximum degree four, for planar graphs with girth five, for bipartite five‐regular graphs, for graphs of diameter three, and for bipartite graphs of diameter four. We show that there exist polynomial‐time algorithms for the following classes of graphs: claw‐free, ‐free, diameter two, bipartite with diameter three, and graphs with bounded treewidth.

Source: Journal of Graph Theory

DOI: 10.1002/jgt.23167

Authors: Valentin Bouquet, Christophe Picouleau

Institutions: Conservatoire National des Arts et Métiers, Centre d'études et de recherche en informatique et communications

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,950

OpenAlex ID: W4403171189

FWCI: 0.974

Cites: 16

Cited by: 5

Related to: 10