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arXiv · 2506.08557

On the maximal matchings of trees

Lingjuan Shi·Wei Li·Kai Deng
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Abstract

An independent edge set of graph $G$ is a matching, and is maximal if it is not a proper subset of any other matching of $G$. The number of all the maximal matchings of $G$ is denoted by $Ψ(G)$. In this paper, an algorithm to count $Ψ(T)$ for a tree $T$ is given. We show that for any tree $T$ with $n$ vertices, $Ψ(T)\geq\lceil\frac{n}{2}\rceil$, and the tree which obtained the lower bound is characterized.

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Lingjuan Shi, Wei Li, Kai Deng. 2025-06-10. On the maximal matchings of trees. https://arxiv.org/abs/2506.08557

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