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An Application of Ramsey's Theorem

Published online by Cambridge University Press:  20 November 2018

E. J. Cockayne
E. J. Cockayne*
Affiliation:
University of Victoria, Victoria, British Columbia
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By an r-graph, we mean a finite set V of elements called vertices and a collection of some of the r-subsets of V called edges with the property that each vertex is incident with at least one edge. An A-chromatic r-graph is an r-graph all of whose edges are coloured A.

Theorem. Let G1, …, Gt denote r-graphs. There exists a nonempty class of r-graphs such that for each if the edges of G are painted arbitrarily in t colours A1, …, At, then for at least one i in {1, …, t}, G has an Ai-chromatic r-subgraph which is isomorphic to Gi.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 145 - 146
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Ryser, H. J., Combinatorial mathematics, Carus Math. Monograph, Math. Assoc. America, 1963.Google Scholar
2. Ramsey, F. P., On a problem of formal logic, Proc. London Math. Soc. (2nd Series) 30 (1930), 264-286.Google Scholar