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arXiv · 2205.13455

Subgraph densities in $K_r$-free graphs

Andrzej Grzesik·Ervin Győri·Nika Salia·Casey Tompkins
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Abstract

In this paper we disprove a conjecture of Lidický and Murphy about the number of copies of a given graph in a $K_r$-free graph and give an alternative general conjecture. We also prove an asymptotically tight bound on the number of copies of any bipartite graph of radius at most $2$ in a triangle-free graph.

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Andrzej Grzesik, Ervin Győri, Nika Salia, Casey Tompkins. 2022-05-26. Subgraph densities in $K_r$-free graphs. https://arxiv.org/abs/2205.13455

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