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The size Ramsey number
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 questionsExpand
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Problems and Solutions
TLDR
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
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On cycle - Complete graph ramsey numbers
TLDR
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
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Ramsey goodness and beyond
TLDR
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
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An extremal problem for paths in bipartite graphs
TLDR
A formula is found for the maximum number of edges in a graph G ⊆ K(a, b) which contains no path P2l for l > c. Expand
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Some Complete Bipartite Graph - Tree Ramsey Numbers
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 notExpand
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A local density condition for triangles
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 followingExpand
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Ramsey Problems Involving Degrees in Edge-colored Complete Graphs of Vertices Belonging to Monochromatic Subgraphs
TLDR
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
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Multipartite graph—Sparse graph Ramsey numbers
TLDR
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
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Extremal problems involving vertices and edges on odd cycles
TLDR
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
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