Work

Local flag algebras

Year: 2026

Type: preprint

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 $Δ(G)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.12461

Authors: Davey, Eoin, Hurley, Eoin, de Verclos, Rémi de Joannis, Kang, Ross J., Volec, Jan

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Universiteit van Amsterdam, Radboud Universiteit, Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Awards: Asymptotic triangle-free structure (3Free), G5093044862, G565383568, On the edge: theory and techniques at the frontiers of edge-colouring

OpenAlex ID: W7168408317

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