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**Zentralblatt MATH**

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

**Zbl.No: ** 695.05048

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

**Title: ** The book-tree Ramsey numbers. (In English)

**Source: ** Sci., Ser. A 1, 111-117 (1988).

**Review: ** Let G and H be two graphs. The Ramsey number r(G,H) is the smallest positive integer p such that coloring the edges of the complete graph on p vertices with two colors results in either a copy of G with all of its edges assigned the first color or a copy of H with all of its edges assigned the second color. The main result in this paper is r(B_{m},T_{n}) = 2n-1 where T_{n} is any tree on n vertices and B_{m} is the book with m pages, i.e. B_{m} = K_{(1,1,m)}. The authors then consider some generalizations of this result.

**Reviewer: ** J.E.Graver

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

**Keywords: ** Ramsey number; complete graph; tree; book

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