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arXiv · 2412.15950

Maximal independent sets in graphs with given matching number

Yongtang Shi·Jianhua Tu·Ziyuan Wang
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Abstract

A maximal independent set in a graph $G$ is an independent set that cannot be extended to a larger independent set by adding any vertex from $G$. 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.

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Yongtang Shi, Jianhua Tu, Ziyuan Wang. 2024-12-20. Maximal independent sets in graphs with given matching number. https://arxiv.org/abs/2412.15950

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