Inducibility of rainbow graphs
Abstract
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 $k!/(k^k-k)$.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.03112
- arXiv:
- arXiv:2405.03112
- Bibcode:
- 2024arXiv240503112C
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 27 pages