The asymptotics of r(4, t)

Abstract

For integers s, t ≥ 2, the Ramsey number r(s, t) denotes the minimum n such that every n-vertex graph contains a clique of order s or an independent set of order t. In this paper we prove r(4, t) = (Formula presented.) as t → ∞, which determines r(4, t) up to a factor of order log2 t, and solves a conjecture of Erdős.