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, is k-good .
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