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Jin's theorem on dense triangle-free graphs

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-20-000012Oct 20, 2026math.COscore 0

A Lean 4 / Mathlib formalization of Jin's theorem: a finite triangle-free graph on n vertices with minimum degree greater than 10n/29 is 3-colourable; and of its sharpness: for every m ≥ 1 the blow-up of the Grötzsch graph with weights 3m, 2m, 4m is a triangle-free 10m-regular graph on 29m vertices that is not 3-colourable (Häggkvist). This extends the case r = 2 of the Andrásfai–Erdős–Sós theorem, which is in Mathlib. Mathlib does not have Jin's theorem.

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