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:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.13189
 arXiv:
 arXiv:2301.13189
 Bibcode:
 2023arXiv230113189A
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 10 pages