Induced subdivisions in graphs of large girth
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913175518052352 |
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| author | Kuang, Peiru Wang, Yan |
| author_facet | Kuang, Peiru Wang, Yan |
| contents | In this paper, we prove that there exists an absolute constant $g_0$ such that, for every integer $k\ge 3$, every graph $G$ with $δ(G)\ge k$ and $g(G)\ge g_0$ contains an induced subdivision of $K_{k+1}$. This fully resolves a problem raised by Kühn and Osthus (originally attributed to Shi), and improves a recent result of Girão and Hunter. Our proof uses some ideas from Girão and Hunter. Another main ingredient in our proof is an induced variant of Mader's theorem: for every fixed \(s,η,D\), every graph \(J\) with \(Δ(J)\le D\), \(d(J)>s-2+η\) and sufficiently large girth contains an induced subdivision of \(K_s\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17218 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Induced subdivisions in graphs of large girth Kuang, Peiru Wang, Yan Combinatorics 05C35 In this paper, we prove that there exists an absolute constant $g_0$ such that, for every integer $k\ge 3$, every graph $G$ with $δ(G)\ge k$ and $g(G)\ge g_0$ contains an induced subdivision of $K_{k+1}$. This fully resolves a problem raised by Kühn and Osthus (originally attributed to Shi), and improves a recent result of Girão and Hunter. Our proof uses some ideas from Girão and Hunter. Another main ingredient in our proof is an induced variant of Mader's theorem: for every fixed \(s,η,D\), every graph \(J\) with \(Δ(J)\le D\), \(d(J)>s-2+η\) and sufficiently large girth contains an induced subdivision of \(K_s\). |
| title | Induced subdivisions in graphs of large girth |
| topic | Combinatorics 05C35 |
| url | https://arxiv.org/abs/2605.17218 |