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


V. Nikiforov


We investigate the following problem of Erdos: Determine the minimum number of k-cliques in a graph of order n with independence number ≤ l. We disprove the original conjecture of Erdos 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.

Publication Title

Combinatorics Probability and Computing