Inducibility of rainbow graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912820559347712 |
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| author | Cairncross, Emily Mizgerd, Clayton Mubayi, Dhruv |
| author_facet | Cairncross, Emily Mizgerd, Clayton Mubayi, Dhruv |
| contents | Fix $k\ge 11$ and a rainbow $k$-clique $R$. We prove that the inducibility of $R$ is $k!/(k^k-k)$. An extremal construction is a balanced recursive blow-up of $R$. This answers a question posed by Huang, that is a generalization of an old problem of Erd\H os and Sós. It remains open to determine the minimum $k$ for which our result is true. More generally, we prove that there is an absolute constant $C>0$ such that every $k$-vertex connected rainbow graph with minimum degree at least $C\log k$ has inducibility $k!/(k^k-k)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inducibility of rainbow graphs Cairncross, Emily Mizgerd, Clayton Mubayi, Dhruv Combinatorics Fix $k\ge 11$ and a rainbow $k$-clique $R$. We prove that the inducibility of $R$ is $k!/(k^k-k)$. An extremal construction is a balanced recursive blow-up of $R$. This answers a question posed by Huang, that is a generalization of an old problem of Erd\H os and Sós. It remains open to determine the minimum $k$ for which our result is true. More generally, we prove that there is an absolute constant $C>0$ such that every $k$-vertex connected rainbow graph with minimum degree at least $C\log k$ has inducibility $k!/(k^k-k)$. |
| title | Inducibility of rainbow graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.03112 |