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Topological cliques in graphs II

Published online by Cambridge University Press:  12 September 2008

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

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
Copyright
Copyright © Cambridge University Press 1996

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References

[1]Ajtai, M., Komlós, J. and Szemerédi, E. (1979) Topological complete subgraphs in random graphs. Studia. Sci. Math. Hung. 14 293297.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 224227.CrossRefGoogle 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 141143.CrossRefGoogle Scholar
[7]Erdős, P. and Hajnal, A. (1969) On complete topological subgraphs of certain graphs. Ann. Univ. Sci. Budapest 1 193199.Google Scholar
[8]Komlós, J. and Szemerédi, E. (1994) Topological cliques in graphs. Combinatorics, Probability & Computing 3 247256.CrossRefGoogle Scholar
[9]Mader, W. (1967) Homomorphieeigenschaften und mittlere Kantendichte von Graphen. Math. Ann. 174 265268.CrossRefGoogle Scholar
[10]Mader, W. (1972) Hinreichende Bedingungen fur die Existenz von Teilgraphen die zu einem vollstandigen Graphen homöomorph sind. Math. Nachr. 53 145150.CrossRefGoogle Scholar
[11]Szemerédi, E. (1976) Regular partitions of graphs. Colloques Internationaux CNRS No. 260 – Problèmes Combinatoires et Thèorie des Graphes Orsay, France, 399401.Google Scholar
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