Open Research Index

Classical bounds for graph Ramsey numbers

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-15-000021Oct 15, 2026math.COscore 0

A Lean 4 / Mathlib formalization of the classical bounds for graph Ramsey numbers: R(3, 3) = 6 (every graph on six vertices has a triangle or three independent vertices, and the pentagon has neither), the Erdős–Szekeres upper bound R(s, t) ≤ C(s + t − 2, s − 1), and Erdős's lower bound R(k, k) > 2^(k/2) for k ≥ 3, proved by a union bound over the edge sets of graphs on n vertices.

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