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(H,k) stable bipartite graphs with minimum size

Aneta Dudek; Małgorzata Zwonek — 2009

Discussiones Mathematicae Graph Theory

Let us call a graph G(H;k) vertex stable if it contains a subgraph H after removing any of its k vertices. In this paper we are interested in finding the $(K_{n, n + 1}; 1)$ (respectively $(K_{n, n}; 1)$ ) vertex stable graphs with minimum size.

(H,k) stable graphs with minimum size

Aneta Dudek; Artur Szymański; Małgorzata Zwonek — 2008

Discussiones Mathematicae Graph Theory

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).

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