On the Minimum Number of k-Cliques in Graphs with Restricted Independence Number
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.
Combinatorics Probability and Computing
Nikiforov, V. (2001). On the Minimum Number of k-Cliques in Graphs with Restricted Independence Number. Combinatorics Probability and Computing, 10 (4), 361-366. https://doi.org/10.1017/S0963548301004722