Annie Raymond: The Lower Boundary of the {K_2, K_p, K_q}-Graph Profile

Annie Raymond (UMass)

We determine the minimum number of cliques that appear in any n-vertex graph with a given number of edges and a given number of cliques of size p. The question of determining the minimum number of r-cliques that appear in any n-vertex graph with a given number of edges was previously resolved by Razborov for r=3, Nikiforov for r=4 and Reiher for all other values of r.  Very recently, Li, Liu and Zhang determined the minimum number of r-cliques when the number of s-cliques is fixed for any s<r. This is joint work with Greg Blekherman.