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

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMGT_2002_22_1_a2,
     author = {Borowiecki, Mieczys{\l}aw and Sidorowicz, El\.zbieta},
     title = {Weakly {P-saturated} graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {17--29},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a2/}
}
TY  - JOUR
AU  - Borowiecki, Mieczysław
AU  - Sidorowicz, Elżbieta
TI  - Weakly P-saturated graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2002
SP  - 17
EP  - 29
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a2/
LA  - en
ID  - DMGT_2002_22_1_a2
ER  - 
%0 Journal Article
%A Borowiecki, Mieczysław
%A Sidorowicz, Elżbieta
%T Weakly P-saturated graphs
%J Discussiones Mathematicae. Graph Theory
%D 2002
%P 17-29
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a2/
%G en
%F DMGT_2002_22_1_a2
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/

[1] B. Bollobás, Weakly k-saturated graphs, in: H. Sachs, H.-J. Voss and H. Walther, eds, Proc. Beiträge zur Graphentheorie, Manebach, 9-12 May, 1967 (Teubner Verlag, Leipzig, 1968) 25-31.

[2] P. Erdős, A. Hajnal and J.W. Moon, A Problem in Graph Theory, Amer. Math. Monthly 71 (1964) 1107-1110, doi: 10.2307/2311408.

[3] R. Lick and A. T. White, k-degenerated graphs, Canadian J. Math. 22 (1970) 1082-1096, doi: 10.4153/CJM-1970-125-1.

[4] P. Mihók, On graphs critical with respect to vertex partition numbers, Discrete Math. 37 (1981) 123-126, doi: 10.1016/0012-365X(81)90146-1.

[5] G. Kalai, Weakly saturated graphs are rigid, Annals of Discrete Math. 20 (1984) 189-190.

[6] P. Turán, On the Theory of Graphs, Colloq. Math. 3 (1954) 19-30.