ON THE NON-(p-1)-PARTITE Kp-FREE GRAPHS.

We say that a graph G is maximal Kp-free if G does not contain Kp but if we add any new edge e ∈ E(Ḡ) to G, then the graph G + e contains Kp. We study the minimum and maximum size of non-(p - 1)-partite maximal Kp-free graphs with n vertices. We also answer the interpolation question: for which values of n and m are there any n-vertex maximal Kp-free graphs of size m? [ABSTRACT FROM AUTHOR]