THE RAMSEY NUMBER R(3,T) HAS ORDER OF MAGNITUDE T(2)/LOG-T

The Ramsey number R(s, t) for positive integers s and t is the minimum integer n for which every red-blue coloring of the edges of a complete n-vertex graph induces either a red complete graph of order s or a blue complete graph of order t. This paper proves that R(3, t) is bounded below by (1 - o(1))t(2)/log t times a positive constant. Together with the known upper bound of (1 + o(1))t(2)/log t, it follows that R(3, t) has asymptotic order of magnitude t(2)/log t. (C) 1995 John Wiley & Sons, Inc.