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arXiv · 2407.17455

An Erdős-Ko-Rado type theorem for subgraphs of perfect matchings

Dániel T. Nagy
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Abstract

Let $M_k$ be a $2n$-vertex graph with $n$ pairwise disjoint edges and let $\mathcal{H}^{(p,s)}(n)$ be the family of subsets of $V(M_n)$ that span exactly $p$ edges and $s$ isolated vertices. We prove that for $n\ge 2p+s$ this family has the Erdős--Ko--Rado property: the size of the largest intersecting family equals to the number of sets containing a fixed vertex. The bound $n\ge 2p+s$ is the best possible, improving a recent theorem with $n\ge 2p+2s$ by Fuentes and Kamat.

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Dániel T. Nagy. 2024-07-24. An Erdős-Ko-Rado type theorem for subgraphs of perfect matchings. https://arxiv.org/abs/2407.17455

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