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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)
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)
It is shown that if G and H are star-forests with no single edge stars, then (G, H) is Ramsey-finite if and only if both G and H are single stars with an odd number of edges. Ramsey-finite or Ramsey-infinite depending on the choice of G, H, k, and l with the general case unsettled. This disproves the conjecture given in [2] where it is suggested that the(More)