Local flag algebras

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 $Δ(G)$.

Disclosure

“neither coding effort used AI assistance. These results were made publicly accessible in 2024 via Eoin Davey’s MSc thesis [5] at the University of Amsterdam theses repository. During the third phase, one commercially available agentic AI system was used for the following purposes: 1. formal verification of the mathematical results in Lean 4; 2. empirical checks to sweep for potential counterexample graphs; 3. proof of subsidiary results (Theorems 1.5 and 1.6) under ou”

PDF page 26

Classification

Proof ideas or individual proof-step assistance

Multiplier

8

Verified

2026-08-23T18:52:22.582658Z

Structural counts