Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-22T05:02:20.198Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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