Let k_r(n,m) denote the minimum number of r-cliques in graphs with n vertices and m edges. For r=3,4 we give a lower bound on k_r(n,m) that approximates k_r(n,m) with an error smaller than n^r/(n^2-2m). The solution is based on a constraint minimization of certain multilinear forms. In our proof, a combinatorial strategy is coupled with extensive analytical arguments.
- Pub Date:
- October 2007
- Mathematics - Combinatorics;
- This interim version is aimed to correct an error in the first version of the paper. The scope of the main result is reduced, but the advantages of the method are still clear