Book Ramsey numbers. I


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. 
DOI: 10.1002/rsa.20081