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**Zentralblatt MATH**

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

**Zbl.No: ** 593.05050

**Autor: ** Erdös, Paul; Faudree, Ralph J.; Rousseau, C.C.; Schelp, R.H.

**Title: ** Multipartite graph-sparse graph Ramsey numbers. (In English)

**Source: ** Combinatorica 5, 311-318 (1985).

**Review: ** Let F and G be finite graphs. The Ramsey number r(F,G) is the smallest positive integer n so that, given any graph on n vertices, either it contains a subgraph isomorphic to F or its complement contains a subgraph isomorphic to G. In this paper, the Ramsey number r(F,G) is determined in the case where F is an arbitrary fixed graph and G is a sufficiently large sparse connected graph with restrictions on the maximum degree of its vertices. An asymptotically correct upper bound is obtained for f(F,T) where T is a sufficiently large, but otherwise arbitrary, tree.

**Reviewer: ** J.E.Graver

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

**Keywords: ** Ramsey number; sufficiently large sparse connected graph

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