{"id":"palomar/PALOMAR-2026-10-16-000024","url":"https://github.com/jtraverso/turan-stability/tree/3eb99033cc931add291781f77b7446dcba8f5f9d","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-16-000024-v1.json","repo":"https://github.com/jtraverso/turan-stability","tags":["math.CO","msc:05C35","msc:05C75","extremal-graph-theory","turan-theorem","stability","lean-formalization"],"score":0,"title":"Füredi's stability theorem and the Erdős–Simonovits stability theorem","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 / Mathlib formalization of the stability theory of Turán's theorem. (1) Füredi's sharp stability theorem for cliques: a K_{p+1}-free graph on n vertices with at least t(n, p) − t edges (t(n, p) the number of edges of the Turán graph) has a p-partite subgraph with at least e(G) − t edges, via Füredi's partition inequality e(G) + Σᵢ e(G[Vᵢ]) ≤ e(K(V₁, …, V_p)); also edit distance at most 3t to a complete p-partite graph. (2) The Erdős–Simonovits stability theorem for every forbidden graph L with χ(L) ≤ p + 1: for every ε > 0 there are δ > 0 and n₀ such that every L-free graph on n ≥…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-16","reactions":{},"formalized":true,"formalizes":[{"title":"A proof of the stability of extremal graphs, Simonovits' stability from Szemerédi's regularity","identifier":"doi:10.1016/j.jctb.2015.05.001","relationship":"formalizes"},{"title":"A method for solving extremal problems in graph theory, stability problems","identifier":"","relationship":"formalizes"},{"title":"Some recent results on extremal problems in graph theory","identifier":"","relationship":"formalizes"},{"title":"The asymptotic number of graphs not containing a fixed subgraph and a problem for hypergraphs having no exponent","identifier":"doi:10.1007/BF01788085","relationship":"formalizes"}]}