Hostname: page-component-76c49bb84f-qtd2s Total loading time: 0 Render date: 2025-07-09T15:49:00.073Z Has data issue: false hasContentIssue false
  • English
  • Français

Complete Subgraphs of r-partite Graphs

Published online by Cambridge University Press:  12 September 2008

Guoping Jin
Guoping Jin
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Cambridge University, England
Get access Rights & Permissions [Opens in a new window]

Abstract

The smallest minimal degree of an r-partite graph that guarantees the existence of a complete subgraph of order r has been found for the case r = 3 by Bollobás, Erdő and Szemerédi, who also gave bounds for the cases r ≥ 4. In this paper the exact value is established for the cases r = 4 and 5, and the bounds for r ≥ 6 are improved.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 3 , September 1992 , pp. 241 - 250
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Bollobás, B. (1978) Extremal Graph Theory, Academic Press, London, p. 488.Google Scholar
[2]Bollobás, B., Erdős, P. and Straus, E. C. (1974) Complete subgraphs of chromatic graphs and hypergraphs. Utilitas Math 6 343–347.Google Scholar
[3]Bollobás, B., Erdős, P. and Szemerédi, E. (1974) On complete subgraphs of r-chromatic graphs. Discrete Math 13 97–107.CrossRefGoogle Scholar
[4]Turán, P. (1941) On an extremal problem in graph theory. Mat. Fiz. Lapok 48 436–452. (Hungarian)Google Scholar