Induced subdivisions of $K_{d+1}$ in graphs of high girth
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908876412026880 |
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| author | Girão, António Hunter, Zach |
| author_facet | Girão, António Hunter, Zach |
| contents | In this paper, we show that for all $k\geq 10^8$, every graph with minimum degree $k$ and girth at least $10^8$ contains an induced subdivision of a $K_{k+1}$. This answers a problem asked by Kühn and Osthus (originally attributed to Shi). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Induced subdivisions of $K_{d+1}$ in graphs of high girth Girão, António Hunter, Zach Combinatorics In this paper, we show that for all $k\geq 10^8$, every graph with minimum degree $k$ and girth at least $10^8$ contains an induced subdivision of a $K_{k+1}$. This answers a problem asked by Kühn and Osthus (originally attributed to Shi). |
| title | Induced subdivisions of $K_{d+1}$ in graphs of high girth |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.09521 |