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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) (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).
Ai et al. (Thu,) studied this question.