GENERALIZED TURAN’S GRAPH THEOREM - Khadzhiivanov, Nikolay; Nenov, Nedyalko (Ann. Sofia Univ. Fac. Math. and Inf., 2004)
Let G be an n-vertex graph and there is a vertex of G which is contained in maximum number of p-cliques, but is not contained in (s+1)-clique, where 2p(s,n). Then the number of p-cliques of G is less than the number of p-cliques in the n-vertex S-partite Tur\’an’s graph T_s(n) or G=T_s(n).