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 $h(G)\le \omega(G)^{3t-3+o(1)}$. This resolves a conjecture of Hajebi, Li and Spirkl (Hitting all maximum stable sets in $P_{5}$-free graphs, JCTB 2024).

翻译：给定图$G$，令$h(G)$表示$V(G)$中与$G$的每个最大独立集均有交的最小子集大小。我们证明：任何不含大小为$t$的诱导匹配的图$G$都满足$h(G)\le \omega(G)^{3t-3+o(1)}$。这解决了Hajebi、Li和Spirkl的一个猜想（Hitting all maximum stable sets in $P_{5}$-free graphs, JCTB 2024）。