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Lovász's perfect graph theorems

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-21-000007Oct 21, 2026math.COscore 0

A Lean 4 / Mathlib formalization of Lovász's 1972 theorems on perfect graphs: a finite simple graph is perfect (every induced subgraph has chromatic number equal to its clique number) if and only if |S| ≤ α(G[S]) · ω(G[S]) for every vertex set S; and the perfect graph theorem conjectured by Berge, that a finite graph is perfect if and only if its complement is perfect. The proof follows Gasparian's linear-algebra argument. Mathlib has chromatic, clique and independence numbers but no perfect graphs.

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