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On the Ramsey Number r(F, Km) Where F is a Forest

Published online by Cambridge University Press:  20 November 2018

Saul Stahl
Saul Stahl*
Affiliation:
Western Michigan University, Kalamazoo, Michigan
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The graphs considered here are finite and have no loops or multiple edges. In particular, Km denotes the complete graph on m vertices. For any graph G,V(G) and E(G) denote, respectively, the vertex and edge sets of G. A forest is a graph which has no cycles and a tree is a connected forest. The reader is referred to [1] or [4] for the meaning of terms not defined in this paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 585 - 589
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Behzad, M. and Chartrand, G., Introduction to the theory of graphs (Allyn and Bacon, Boston, 1971).Google Scholar
2. Burr, S. A., Generalized Ramsey theory for graphs—a survey, Graphs and Combinatorics, Proceedings of the Capital Conference on Graph Theory and Combinatorics at the George Washington University, June 18-22, 1973, 52–76 (Springer-Verlag, New York, 1974).Google Scholar
3. Chvâtal, V., On the Ramsey numbers r(Km, T) (to appear).Google Scholar
4. Harary, F., Graph theory (Addison-Wesley, Reading, 1969).Google Scholar
5. Lick, D. R. and White, A. T., k-degenerate graphs, Can. J. Math 22 (1970), 1082–1096,Google Scholar