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 -free graphs, but that there exists an integer for which it is NP-complete for -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