Piercing independent sets in graphs without large induced matching
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910389750464512 |
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| author | Ai, Jiangdong Liu, Hong Xu, Zixiang Zhou, Qiang |
| author_facet | Ai, Jiangdong Liu, Hong Xu, Zixiang Zhou, Qiang |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Piercing independent sets in graphs without large induced matching Ai, Jiangdong Liu, Hong Xu, Zixiang Zhou, Qiang Combinatorics Computational Geometry 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). |
| title | Piercing independent sets in graphs without large induced matching |
| topic | Combinatorics Computational Geometry |
| url | https://arxiv.org/abs/2403.19737 |