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,K1,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,K1,2) 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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