Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  593.05050
Autor:  Erdös, Paul; Faudree, Ralph J.; Rousseau, C.C.; Schelp, R.H.
Title:  Multipartite graph-sparse graph Ramsey numbers. (In English)
Source:  Combinatorica 5, 311-318 (1985).
Review:  Let F and G be finite graphs. The Ramsey number r(F,G) is the smallest positive integer n so that, given any graph on n vertices, either it contains a subgraph isomorphic to F or its complement contains a subgraph isomorphic to G. In this paper, the Ramsey number r(F,G) is determined in the case where F is an arbitrary fixed graph and G is a sufficiently large sparse connected graph with restrictions on the maximum degree of its vertices. An asymptotically correct upper bound is obtained for f(F,T) where T is a sufficiently large, but otherwise arbitrary, tree.
Reviewer:  J.E.Graver
Classif.:  * 05C55 Generalized Ramsey theory
Keywords:  Ramsey number; sufficiently large sparse connected graph

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