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**Zentralblatt MATH**

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

**Zbl.No: ** 432.05038

**Autor: ** Burr, Stefan A.; Erdös, Paul; Faudree, Ralph J.; Schelp, R.H.

**Title: ** A class of Ramsey-finite graphs. (In English)

**Source: ** Proc. 9th southeast. Conf. on Combinatorics, graph theory, and computing, Boca Raton 1978, 171-180 (1978).

**Review: ** [For the entire collection see Zbl 396.00003.]

The notation F ––> (G,H) is used to imply that if the edges of Fare colored with two colors, say red and blue, then either there exists a red copy of G or a blue copy of H. The class of all graphs F or which F ––> (G,H) is denoted R'(G,H). The class of minimal graphs in R'(G,H) is denoted R(G,H). The authors show that if G is an aritrary graph on n vertices and m is a positive integer, then whenever F in R(mK_{2},G), we always have |E(F)| \leq **sum**_{i = 1}^{b}n^{i} where b = (m-1)(\binom{2m-1}{2})+1)+1. As a corollary, they conclude that he class R(mK_{2},G) is finite. It should be noted that there are large classes of graphs for which R(G,H) is infinite but few nontrivial examples are known where R(G,H) is finite.

**Reviewer: ** W.T.Trotter

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

**Keywords: ** minimal graphs

**Citations: ** Zbl.396.00003

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