Maximal independent sets in graphs with given matching number
Combinatorics
2025-06-02 v2
Abstract
A maximal independent set in a graph is an independent set that cannot be extended to a larger independent set by adding any vertex from . This paper investigates the problem of determining the maximum number of maximal independent sets in terms of the matching number of a graph. We establish the maximum number of maximal independent sets for general graphs, connected graphs, triangle-free graphs, and connected triangle-free graphs with a given matching number, and characterize the extremal graphs achieving these maxima.
Keywords
Cite
@article{arxiv.2412.15950,
title = {Maximal independent sets in graphs with given matching number},
author = {Yongtang Shi and Jianhua Tu and Ziyuan Wang},
journal= {arXiv preprint arXiv:2412.15950},
year = {2025}
}