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Topological Cliques in Graphs

Published online by Cambridge University Press:  12 September 2008

János komlós  and
Endre Szemerédi
János komlós
Affiliation:
Rutgers University and Hungarian Academy of Sciences
Endre Szemerédi
Affiliation:
Rutgers University and Hungarian Academy of Sciences
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Abstract

Let f(t) be the largest integer such that every graph with average degree t has a topological clique with f(i) vertices. It is widely believed that . Here we prove the weaker estimate .

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 2 , June 1994 , pp. 247 - 256
Copyright
Copyright © Cambridge University Press 1994

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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, 293–297.Google Scholar
[2]Bollobás, B. (1978) Extremal Graph Theory, Academic Press, London.Google Scholar
[3]Bollobás, B. and Catlin, P. (1981) Topological cliques of random graphs. J. Combinatorial Theory 30B, 224–227.CrossRefGoogle Scholar
[4]Erdős, P. and Fajtlowicz, S. (1981) On the conjecture of Hajós. Combinatorica 1, 141–143.CrossRefGoogle Scholar
[5]Erdős, P. and Hajnal, A. (1969) On complete topological subgraphs of certain graphs. Annales Univ. Sci. Budapest 7, 193–199.Google Scholar
[6]Komlós, J. and Sós, V. (manuscript) Regular subgraphs of graphs.Google Scholar
[7]Lov´sz, L. (1979) Combinatorial Problems and Exercises, Akadémiai Kiadó, Budapest.Google Scholar
[8]Mader, W. (1967) Homomorphieeigenschaften und mittlere Kantendichte von Graphen. Math. Annalen 174, 265–268.CrossRefGoogle Scholar
[9]Mader, W. (1972) Hinreichende Bedingungen fur die Existenz von Teilgraphen die zu einem vollständigen Graphen homöomorph sind. Math. Nachr. 53, 145–150.CrossRefGoogle Scholar
[10]Szemerédi, E. (1976) Regular partitions of graphs. Colloques Internationaux C.N.R.S. N° – 260 - Problèmes Combinatoires et Théorie des Graphes, Orsay, 399–401.Google Scholar
[11]Szemerédi, E. (1975) On a set containing no k elements in arithmetic progression. Acta Arithmetica XXVII, 199–245.CrossRefGoogle Scholar