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On the Minimum Number of k-Cliques in Graphs with Restricted Independence Number

Published online by Cambridge University Press:  02 October 2001

V. NIKIFOROV
V. NIKIFOROV
Affiliation:
Beli brezi bl. 2, Sofia 1680, Bulgaria (e-mail: vladon@otel.net)
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Abstract

We investigate the following problem of Erdős:

Determine the minimum number of k-cliques in a graph of order n with independence number [ges ] l.

We disprove the original conjecture of Erdős which was stated in 1962 for all but a finite number of pairs k, l, and give asymptotic estimates for l = 3, k [ges ] 4, and l = 4, k [ges ] 4.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 4 , July 2001 , pp. 361 - 366
Copyright
2001 Cambridge University Press

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