Let denote the class of all graphsG which satisfyG→(G1,G2). As a way of measuring minimality for members of, we define thesize Ramsey number ř(G1,G2) by.We then investigate various questions… Expand

Edited by Gerald A. West with the collaboration of Itshak Borosh, Paul Bracken, Ezra A. Gessel, László Lipták, Frederick W. Miles, Richard Pfiefer, Dave Renfro, Cecil C. Rousseau, Leonard Smiley, Kenneth Stolarsky, Richard Stong, Walter Stromquist, Daniel Ullman, Charles Vanden Eynden, Sam Vandervelde, and Fuzhen Zhang.Expand

A new upper bound is given for the cycle-complete graph Ramsey number r(C,,,, K), the smallest order for a graph which forces it to contain either a cycle of order m or a set of ri independent vertices.Expand

In a seminal paper from 1983, Burr and Erdős started the systematic study of Ramsey numbers of cliques vs. large sparse graphs, raising a number of problems.Expand

We investigate r(Ka,a,, T) for a = 2 and a = 3, where T is an arbitrary tree of order n. For a = 2, this Ramsey number is completely determined by r(K2,2, K1,m) where m = Δ(T). For a = 3, we do not… Expand

Let G be a graph on n vertices and let ? and β be real numbers, 0 < ?, β < 1. Further, let G satisfy the condition that each ??n? subset of its vertex set spans at least βn2 edges. The following… Expand

We consider monochromatic subragraphs in two-colored graphs as guaranteed by Ramsey's theorem, and ask various questions concerning the degree in the two- colored complete graphs of vertices which are part of these subgraphs.Expand

The Ramsey numberr(F, G) is determined in the case whereF is an arbitrary fixed graph andG is a sufficiently large sparse connected graph with a restriction on the maximum degree of its vertices.Expand

We investigate the minimum, taken over all graphs G with n vertices and at least ⌊ n 2 /4⌋ + 1 edges, of the number of Vertices and edges of G which are on cycles of length 2 k + 1.Expand