Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-18T10:02:05.856Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological cliques in graphs II

Published online by Cambridge University Press:  12 September 2008

János Komlós  and
Endre Szemerédi
János Komlós
Affiliation:
Rutgers University Mathematical Institute, Hungarian Academy of Sciences, Reáltanoda u. 13–15 H-1053 Budapest, Hungary
Endre Szemerédi
Affiliation:
Rutgers University Mathematical Institute, Hungarian Academy of Sciences, Reáltanoda u. 13–15 H-1053 Budapest, Hungary
Get access Rights & Permissions [Opens in a new window]

Abstract

This note contains a refinement of our paper [8], leading to an alternative proof of a conjecture of Mader and of Erdős and Hajnal recently proved by Bollobás and Thomason.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 1 , March 1996 , pp. 79 - 90
Copyright
Copyright © Cambridge University Press 1996

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.)

References

[1]Ajtai, M., Komlós, J. and Szemerédi, E. (1979) Topological complete subgraphs in random graphs. Studia. Sci. Math. Hung. 14 293–297.Google Scholar
[2]Alon, N. and Seymour, P. (1994) Private communication (see [8]).Google Scholar
[3]Bollobás, B. (1978) Extremal Graph Theory, Academic Press.Google Scholar
[4]Bollobás, B. and Catlin, P. (1981) Topological cliques of random graphs. J. Combinatorial Theory (B) 30 224–227.Google Scholar
[5]Bollobás, B. and Thomason, A. Topological complete subgraphs. (Manuscript.)Google Scholar
[6]Erdős, P. and Fajtlowicz, S. (1981) On the conjecture of Hajós. Combinatorica 1 141–143.Google Scholar
[7]Erdős, P. and Hajnal, A. (1969) On complete topological subgraphs of certain graphs. Ann. Univ. Sci. Budapest 1 193–199.Google Scholar
[8]Komlós, J. and Szemerédi, E. (1994) Topological cliques in graphs. Combinatorics, Probability & Computing 3 247–256.Google Scholar
[9]Mader, W. (1967) Homomorphieeigenschaften und mittlere Kantendichte von Graphen. Math. Ann. 174 265–268.CrossRefGoogle Scholar
[10]Mader, W. (1972) Hinreichende Bedingungen fur die Existenz von Teilgraphen die zu einem vollstandigen Graphen homöomorph sind. Math. Nachr. 53 145–150.Google Scholar
[11]Szemerédi, E. (1976) Regular partitions of graphs. Colloques Internationaux CNRS No. 260 – Problèmes Combinatoires et Thèorie des Graphes Orsay, France, 399–401.Google Scholar