On the Non-(p−1)-Partite Kp-Free Graphs
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 1, p. 9.

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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(G) 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?
Classification : 05C35
Mots-clés : extremal problems, maximal Kp-free graphs, Kp-saturated graphs, maximal -free graphs, -saturated graphs 
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Kinnari Amin; Jill Faudree; Ronald J. Gould; Elżbieta Sidorowicz. On the Non-(p−1)-Partite Kp-Free Graphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 1, p. 9. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_1_267782/