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On the Number of Complete Subgraphs of a Graph

Published online by Cambridge University Press:  20 November 2018

J. W. Moon
J. W. Moon*
Affiliation:
University of Alberta, Edmonton
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A graph Gn consists of n nodes some pairs of which are joined by a single edge. A complete k-graph has k nodes and edges. Erdos [1] proved that if a graph Gn has edges, then it contains at least complete 3-graphs if it contains any at all. The main object of this note is to extend this result to complete k-graphs.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 6 , December 1965 , pp. 831 - 834
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Erdös, P., On the number of triangles contained in certain graphs, Canad. Math. Bull. 7 (1964) 53-56.Google Scholar
2. Moon, J. W. and Moser, L., On a problem of Turán, Publ. Math. Inst. Hung. Acad. Sci. 7 (1962) 283-286.Google Scholar
3. Nordhaus, E.A. and Stewart, B. M., Triangles in an ordinary graph, Canad. J. Math. 15 (1963) 33-41.Google Scholar
4. Turán, P., On the theory of graphs, Colloq. Math. 3(1954) 19-30.Google Scholar