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

Authors:
V. Nikiforov
Affiliations:
Beli brezi bl. 2, Sofia 1680, Bulgaria (e-mail: vladon@otel.net)
Venue:
Combinatorics, Probability and Computing
Year:
2001

Citing 2
Cited 1

The Ramsey number R(3, t) has order of magnitude t2/log t

Random Structures & Algorithms
Extremal Graph Theory

Extremal Graph Theory

A problem of Erdős on the minimum number of k-cliques

Journal of Combinatorial Theory Series B

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Abstract

We investigate the following problem of Erdös:Determine the minimum number of k-cliques in a graph of order n with independence number ≥ l.We disprove the original conjecture of Erdös which was stated in 1962 for all but a finite number of pairs k, l, and give asymptotic estimates for l = 3, k ≥ 4, and l = 4, k ≥ 4.