Stefan A. Burr

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1 . Introduction If F, G, and H are (finite, simple) graphs, write F-(G,H) to mean that if the edges of F are colored red and blue (say) in any fashion, then either the red subgraph of F contains a copy of G or the blue subgraph contains H . Write F G for F } (G,G) . A natural question to consider is that of characterizing those F for which F 3 (G,H) for a(More)
Let G be a graph with chromatic number x a °d with t being the minimum number of points in any color class of any point-coloring of G with x colors. Let H be any connected graph and let Hn be a graph on n points which is homeomorphic to H. It is proved that if n is large enough, the Ramsey number r{G, Hn) satisfies r(G, Hn) = (x — l)(n —l) + r. It is also(More)
Chvátal has shown that if T is a tree on n points then r(Kk , T) _ (k 1 ) (n 1 ) + 1 , where r is the (generalized) Ramsey number. It is shown that the same result holds when T is replaced by many other graphs. Such a T is called kgood. The results proved all support the conjecture that any large graph that is sufficiently sparse, in the appropriate sense,(More)
If G and H are graphs, define the Ramsey number r(G, H) to be the least number p such that if the edges of the complete graph Kp are colored red and blue (say), either the red graph contains G as a subgraph or the blue graph contains H. Let mG denote the union of m disjoint copies of G . The following result is proved : Let G and H have k and I points(More)
A typical problem arising in Ramsey graph theory is the following . For given graphs G and L, how few colors can be used to color the edges of G in order that no monochromatic subgraph isomorphic to L is formed? In this paper we investigate the opposite extreme . That is, we will require that in any subgraph of G isomorphic to L, all its edges have(More)
If G and H are graphs, define the Ramsey number to be the least number p such that if the lines of the complete graph Kp are colored red and blue (say),either the red subgraph contains a copy of G or the blue subgraph contains H . Also set r(G) = r(G,G) ; these are called the diagonal Ramsey numbers . These definitions are taken from Chvátal and Harary [1J(More)