# (H,k) stable graphs with minimum size

Aneta Dudek; Artur Szymański; Małgorzata Zwonek

Discussiones Mathematicae Graph Theory (2008)

- Volume: 28, Issue: 1, page 137-149
- ISSN: 2083-5892

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topAneta Dudek, Artur Szymański, and Małgorzata Zwonek. "(H,k) stable graphs with minimum size." Discussiones Mathematicae Graph Theory 28.1 (2008): 137-149. <http://eudml.org/doc/270227>.

@article{AnetaDudek2008,

abstract = {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), $Q(K_\{1,p\},k)$ and Q(Kₛ,k).},

author = {Aneta Dudek, Artur Szymański, Małgorzata Zwonek},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph; stable graph; stable graphs; minimum size; cycles; complete graphs},

language = {eng},

number = {1},

pages = {137-149},

title = {(H,k) stable graphs with minimum size},

url = {http://eudml.org/doc/270227},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Aneta Dudek

AU - Artur Szymański

AU - Małgorzata Zwonek

TI - (H,k) stable graphs with minimum size

JO - Discussiones Mathematicae Graph Theory

PY - 2008

VL - 28

IS - 1

SP - 137

EP - 149

AB - 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), $Q(K_{1,p},k)$ and Q(Kₛ,k).

LA - eng

KW - graph; stable graph; stable graphs; minimum size; cycles; complete graphs

UR - http://eudml.org/doc/270227

ER -

## References

top- [1] P. Frankl and G.Y. Katona, Extremal k-edge-hamiltonian hypergraphs, accepted for publication in Discrete Math. Zbl1182.05089
- [2] I. Horváth and G.Y. Katona, Extremal stable graphs, manuscript. Zbl1228.05187
- [3] R. Greenlaw and R. Petreschi, Cubic Graphs, ACM Computing Surveys, No. 4, (1995).

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