The Ramsey number R(3, t) has order of magnitude t2/log t

  • Authors:

  • Jeong Han Kim

  • Affiliations:

  • Mathematical Science Research Center, AT&T Bell Laboratories, Murray Hill, NJ 07974

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 1995

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Abstract

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))t2/log t, it follows that R(3, t) has asymptotic order of magnitude t2/log t. © 1995 John Wiley & Sons, Inc.