I have the following problem, suppose we have a graph G of n elements, with the property that if we add one missing vertex v, we will get a complete subgraph with s elements K_s of G, in which v belongs to G'. In other words every subgraph of s elements of G is almost a complete graph except for at most one missing vertex. (s is fixed btw). The problem is to prove that |E(G)| >= C(n,2) - C(n-s+2,2), |E(G)| is the number of edges of G. C(n,k) is the binomial coeficient. I am not sure if this is the appropiate forum for this kind of questions, but couldn't find any adequate subforum. Any help is appreciated.