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(Bm,Tn) = 2n-1

where Tn is any tree on n vertices and Bm is the book with m pages, i.e. Bm = 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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