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arXiv · 2301.13189

Localised graph Maclaurin inequalities

Lucas Aragão·Victor Souza
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Abstract

The Maclaurin inequalities for graphs are a broad generalisation of the classical theorems of Tur\'an and Zykov. In a nutshell they provide an asymptotically sharp answer to the following question: what is the maximum number of cliques of size $q$ in a $K_{r+1}$-free graph with a given number of cliques of size $s$? We prove an extensions of the graph Maclaurin inequalities with a weight function that captures the local structure of the graph. As a corollary, we settle a recent conjecture of Kirsch and Nir, which simultaneously encompass the previous localised results of Brada\v{c}, Malec and Tompkins and of Kirsch and Nir.

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Lucas Aragão, Victor Souza. 2023-01-30. Localised graph Maclaurin inequalities. https://arxiv.org/abs/2301.13189

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