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arXiv · 2607.12461

Local flag algebras

Eoin Davey·Eoin Hurley·Rémi de Joannis de Verclos·Ross J. Kang·Jan Volec
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Abstract

We introduce local flag algebras, a variant of Razborov's flag algebra framework in which densities are normalised by the maximum degree $Δ(G)$ rather than the order $|G|$. The framework supports the same semidefinite-method machinery as the classical version, but is tailored to extremal problems that scale with the maximum degree. As an illustrative first application we bound the number of pentagons in a triangle-free graph $G$ as a function of $|G|$ and $Δ(G)$.

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Eoin Davey, Eoin Hurley, Rémi de Joannis de Verclos, Ross J. Kang, Jan Volec. 2026-07-14. Local flag algebras. https://arxiv.org/abs/2607.12461

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