Let us call a G (H,k) graph vertex stable if it contains a subgraph H ever after removing any of its k vertices. By Q(H,k) we will denote the minimum size of an (H,k) vertex stable graph. In this paper, we are interested in finding Q(₃,k), Q(₄,k), and Q(Kₛ,k).
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1397,
author = {Aneta Dudek and Artur Szyma\'nski and Ma\l gorzata Zwonek},
title = {(H,k) stable graphs with minimum size},
journal = {Discussiones Mathematicae Graph Theory},
volume = {28},
year = {2008},
pages = {137-149},
zbl = {1152.05035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1397}
}
Aneta Dudek; Artur Szymański; Małgorzata Zwonek. (H,k) stable graphs with minimum size. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 137-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1397/
[000] [1] P. Frankl and G.Y. Katona, Extremal k-edge-hamiltonian hypergraphs, accepted for publication in Discrete Math. | Zbl 1182.05089
[001] [2] I. Horváth and G.Y. Katona, Extremal stable graphs, manuscript. | Zbl 1228.05187
[002] [3] R. Greenlaw and R. Petreschi, Cubic Graphs, ACM Computing Surveys, No. 4, (1995).