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**Zentralblatt MATH**

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

**Zbl.No: ** 571.05035

**Autor: ** Burr, Stefan A.; Erdös, Paul; Faudree, Ralph J.; Rousseau, C.C.

**Title: ** The Ramsey number for the pair complete bipartite graph-graph of limited degree. (In English)

**Source: ** Graph theory with applications to algorithms and computer science, Proc. 5th Int. Conf., Kalamazoo/Mich. 1984, 163-174 (1985).

**Review: ** [For the entire collection see Zbl 564.00004.]

Let F and G be finite connected graphs. The Ramsey number r(F,G) is defined to be the smallest integer r so that, if the edges of the complete graph on r vertices are colored with two colors, then either there is a copy of F with all of its edges colored with the first or a copy of G colored with the second color. Fix F and define G to be F-good if r(F,G) = (\chi (F)-1)(p(G)-1)+s(F), where \chi(F) is the vertex chromatic number of F, p(G) is the number of vertices of G and s(F) is the smallest number of vertices in some color class of F, under all \chi(F) vertex colorings of F. Let F be a complete bipartite graph. This paper gives conditions on a graph G under which it will be F-good.

**Reviewer: ** J.E.Graver

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

**Keywords: ** Ramsey number; vertex colorings; complete bipartite graph; F-good

**Citations: ** Zbl 564.00004

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