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arXiv · 2304.12565

Matching extension and matching exclusion via the size or the spectral radius of graphs

Shujing Miao·Shuchao Li·Wei Wei
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Abstract

A graph $G$ is said to be $k$-extendable if every matching of size $k$ in $G$ can be extended to a perfect matching of $G$, where $k$ is a positive integer. We say $G$ is $1$-excludable if for every edge $e$ of $G$, there exists a perfect matching excluding $e$. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of $G$ to guarantee that $G$ is $k$-extendable. Then we determine a lower bound on the size (resp. the spectral radius) of $G$ to guarantee that $G$ is $1$-excludable. All the corresponding extremal graphs are characterized.

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Shujing Miao, Shuchao Li, Wei Wei. 2023-04-25. Matching extension and matching exclusion via the size or the spectral radius of graphs. https://arxiv.org/abs/2304.12565

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