Title

Book Ramsey numbers. I

Abstract

A book Bp is a graph consisting of p triangles sharing a common edge. In this paper we prove that if p ≤ q/6 -o(q) and q is large, then the Ramsey number r (BP,Bq) is given by r (BP, Bq) = 2q+3, and the constant 1/6 is essentially best possible. Our proof is based on Szemerédi's uniformity lemma and a stability result for books. © 2005 Wiley Periodicals, Inc.

Publication Title

Random Structures and Algorithms

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