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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.08557 |
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Table of Contents:
- 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.