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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 given G and H. This question is in general extremely difficult, although in 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 H n 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, H n) satisfies r(G, H n) = (x — l)(n —l) + r. It is(More)
It is shown that the classical Ramsey numbers T(m, ta) satisfy r(m,n) 2: r(m,n-1) + 2m-3, and.forl <k<n-2. r(m,n) >r(m,n-k)+r(m,k+ 1)-l. Consequences of the first result for some generalized Ramsey numbers will be considered. If m and n are integers 2 2, define the (classical) Ramsey number r(m, n) to be at least integer t such that if the edges of the(More)
A connected graph G of order n is called m-good if r(Km ,G) = (m-1)(n-1) + 1. Let f(m,n) be the largest integer q such that every connected graph of order n and size q is m-good and let g(m,n) be the largest q for which there exists a connected graph G of order n and size q which is m-good. Asymptotic bounds are given for f and g. 1. Tntroduction. One of(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 k-good. The results proved all support the conjecture that any large graph that is sufficiently sparse, in the appropriate sense,(More)
To test the hypothesis that altered neuronal activity may influence the extent and severity of the glio-vascular lesions produced by 1,3-dinitrobenzene (DNB), rats were either given the tremorgenic pyrethroid, Bifenthrin, or anaesthetised during various dosing schedules of DNB. When compared with controls dosed only with DNB, Bifenthrin tremor made both the(More)