Piercing independent sets in graphs without large induced matching

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)≤ ω(G)³ᵗ⁻³⁺ᵒ⁽¹⁾. This resolves a conjecture of Hajebi, Li and Spirkl (Hitting all maximum stable sets in P₅-free graphs, JCTB 2024).