Proof demonstrates that connected rainbow graphs exhibit inducibility k!/(k^k-k) under degree conditions.
We prove that there is an absolute constant C\,>\,0 such that every k -vertex connected rainbow graph R with minimum degree at least Clog k has inducibility k!/(kᵏ-k) . The same result holds if k≥ 11 , and R is a clique. This answers a question posed by Huang, that is a generalisation of an old problem of Erdös and Sós. It remains open to determine the minimum k for which this is true.
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Cairncross et al. (2025) studied this question.
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