A note on Ramsey numbers for books


The book with n pages Bn is the graph consisting of n triangles sharing an edge. The book Ramsey number r(Bm, Bn) is the smallest integer r such that either Bm ⊂ G or Bn ⊂ Ḡ for every graph G of order r. We prove that there exists a positive constant c such that r(Bm, Bn)= 2n + 3 for all n ≥ cm. Our proof is based mainly on counting; we also use a result of Andrásfai, Erdos, and Sós stating that triangle-free graphs of order n and minimum degree greater than 2n/5 are bipartite. © 2005 Wiley Periodicals, Inc.

Publication Title

Journal of Graph Theory