English

A note on Matching-Cut in $P_t$-free Graphs

Combinatorics 2022-05-17 v3 Discrete Mathematics Data Structures and Algorithms

Abstract

A matching-cut of a graph is an edge cut that is a matching. The problem Matching-Cut is that of recognizing graphs with a matching-cut and is NP-complete, even if the graph belongs to one of a number of classes. We initiate the study of Matching-Cut for graphs without a fixed path as an induced subgraph. We show that Matching-Cut is in P for P5P_5-free graphs, but that there exists an integer t>0t > 0 for which it is NP-complete for PtP_{t}-free graphs.

Keywords

Cite

@article{arxiv.2111.12011,
  title  = {A note on Matching-Cut in $P_t$-free Graphs},
  author = {Carl Feghali},
  journal= {arXiv preprint arXiv:2111.12011},
  year   = {2022}
}

Comments

7 pages, 3 figures; incorporated referees' suggestions

R2 v1 2026-06-24T07:49:20.614Z