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**Zentralblatt MATH**

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

**Zbl.No: ** 438.05046

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

**Title: ** Ramsey-minimal graphs for the pair star, connected graph. (In English)

**Source: ** Stud. Sci. Math. Hung. 15, 265-273 (1980).

**Review: ** Let F, G and H be graphs (without loops or multiple edges). We write F ––> (G,H) if whenever each edge of F is colored either red or blue, then either the red subgraph of F, denoted (F)_{R}, contains a copy of G or the blue subgraph of F, denoted (F)_{B}, contains a copy of H. The graph F is (G,H)-minimal if F ––> (G,H) but F' (not)––> (G,H) for any proper subgraph F' or F. The pair (G,H) will be called Ramsey-finite or Ramsey-infinite depending upon the number of such pairs. In this paper it is proved that (H,K_{1,k}) is Ramsey-infinite for any non-trivial two-connected graph G and any star with k \geq 2 edges. Also it is shown that (H,K_{1,2}) is Ramsey-infinite if H is a bridgeless connected graph.

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

**Keywords: ** Ramsey-minimal graphs; Ramsey-finite; Ramsey-infinite

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