Piercing independent sets in graphs without large induced matching
<|reference_start|>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 $h(G)\le \omega(G)^{3t-3+o(1)}$. This resolves a conjecture of Hajebi, Li and Spirkl (Hitting all maximum stable sets in $P_{5}$-free graphs, JCTB 2024).<|reference_end|>
@article{ai2024piercing,
    title={Piercing independent sets in graphs without large induced matching},
    author={Jiangdong Ai, Hong Liu, Zixiang Xu, Qiang Zhou},
    journal={arXiv preprint arXiv:2403.19737},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.19737},
    primaryClass={math.CO cs.CG}
}