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**Zentralblatt MATH**

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

**Zbl.No: ** 382.05043

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

**Title: ** Ramsey-minimal graphs for multiple copies. (In English)

**Source: ** Nederl. Akad. Wet., Proc., Ser. A 81, 187-195 (1978).

**Review: ** The authors use the notation F ––> (G,H) to indicate that if the edges of the graph F are colored with two colors, say red and blue, then either the red subgraph of F contains a copy of G or the blue subgraph of F contains a copy of H. The class of all graphs F for which F ––> (G,H) is denoted R(G,H). In the case where G = mK_{1,k} and H = nK_{1,\ell}, the authors show that he minimum number of edges in the graph in R(G,H) is (m+n-1)(k+\ell-1). The authors then give a conjecture for the correct formula where G and H are arbitrary star forests. The authors also ask if F ––> (nG,nG), must F contain r(nG,nG)/|V(G)| copies of G.

**Reviewer: ** W.T.Trotter

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

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