Localised graph Maclaurin inequalities
Abstract
The Maclaurin inequalities for graphs are a broad generalisation of the classical theorems of Turán 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 Bradač, Malec and Tompkins and of Kirsch and Nir.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- 10.48550/arXiv.2301.13189
- arXiv:
- arXiv:2301.13189
- Bibcode:
- 2023arXiv230113189A
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 10 pages