Local flag algebras

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

Local flag algebras

Combinatorics 2026-07-14 v1 Discrete Mathematics

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

Abstract

We introduce local flag algebras, a variant of Razborov's flag algebra framework in which densities are normalised by the maximum degree $\Delta(G)$ 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 $\Delta(G)$ .

Cite

@article{arxiv.2607.12461,
  title  = {Local flag algebras},
  author = {Eoin Davey and Eoin Hurley and Rémi de Joannis de Verclos and Ross J. Kang and Jan Volec},
  journal= {arXiv preprint arXiv:2607.12461},
  year   = {2026}
}

Comments

30 pages, 1 figure