Geodesic
Weakly P-saturated graphs
Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 1, pp. 17-29

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For a hereditary property let k_(G) denote the number of forbidden subgraphs contained in G. A graph G is said to be weakly -saturated, if G has the property and there is a sequence of edges of G̅, say e₁,e₂,...,e_l, such that the chain of graphs G = G₀ ⊂ G_0 + e₁ ⊂ G₁ + e₂ ⊂ ... ⊂ G_l-1 + e_l = G_l = K_n(G_i+1 = G_i + e_i+1) has the following property: k_(G_i+1) > k_(G_i), 0 ≤ i ≤ l-1.
Keywords: graph, extremal problems, hereditary property, weakly saturated graphs 
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Borowiecki, Mieczysław; Sidorowicz, Elżbieta. Weakly P-saturated graphs. Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 1, pp. 17-29. http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a2/