Füredi's stability theorem and the Erdős–Simonovits stability theorem
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 ≥…
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