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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 513.05040

**Autor: ** Burr, Stefan A.; Erdös, Paul

**Title: ** Generalizations of a Ramsey-theoretic result of Chvatal. (In English)

**Source: ** J. Graph Theory 7, 39-51 (1983).

**Review: ** Author's abstract: ``Chvátal has shown that if T is a tree on n points then r(K_{k},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, is k-good.''

**Reviewer: ** S.Stahl

**Classif.: ** * 05C55 Generalized Ramsey theory

**Keywords: ** sparse graph; complete graph; generalized Ramsey number

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