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Topological Cliques in Graphs

Published online by Cambridge University Press:  12 September 2008

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

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 .

Type
Research Article
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, 293297.Google Scholar
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