A book of size q is the union of q triangles sharing a common edge. We find
the exact Ramsey number of books of size q versus books of size p when
p<q/6-o(q).Comment: 21 pages. Submitte

Nikiforov, Vladimir

Rousseau, Cecil

English

arXiv

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\u27s uniformity lemma and a stability result for books. © 2005 Wiley Periodicals, Inc

Book Ramsey numbers I

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