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arXiv · 2006.16150

Generalized Turán problems for small graphs

Dániel Gerbner
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Abstract

For graphs $H$ and $F$, the generalized Turán number $ex(n,H,F)$ is the largest number of copies of $H$ in an $F$-free graph on $n$ vertices. We consider this problem when both $H$ and $F$ have at most four vertices. We give sharp results in almost all cases, and connect the remaining cases to well-known unsolved problems. Our main new contribution is applying the progressive induction method of Simonovits for generalized Turán problems.

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Dániel Gerbner. 2020-06-29. Generalized Turán problems for small graphs. https://arxiv.org/abs/2006.16150

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