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arXiv · 2403.19737

Piercing independent sets in graphs without large induced matching

Jiangdong Ai·Hong Liu·Zixiang Xu·Qiang Zhou
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Abstract

Given a graph $G$, denote by $h(G)$ the smallest size of a subset of $V(G)$ which intersects every maximum independent set of $G$. We prove that any graph $G$ without induced matching of size $t$ satisfies $h(G)\le ω(G)^{3t-3+o(1)}$. This resolves a conjecture of Hajebi, Li and Spirkl (Hitting all maximum stable sets in $P_{5}$-free graphs, JCTB 2024).

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Jiangdong Ai, Hong Liu, Zixiang Xu, Qiang Zhou. 2024-03-28. Piercing independent sets in graphs without large induced matching. https://arxiv.org/abs/2403.19737

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