On $(K_{q},k)$ Stable Graphs with Small $k$
نویسندگان
چکیده
منابع مشابه
On (Kq, k) Stable Graphs with Small k
A graph G is (Kq, k) stable if it contains a copy of Kq after deleting any subset of k vertices. In a previous paper we have characterized the (Kq, k) stable graphs with minimum size for 3 6 q 6 5 and we have proved that the only (Kq, k) stable graph with minimum size is Kq+k for q > 5 and k 6 3. We show that for q > 6 and k 6 q 2 + 1 the only (Kq, k) stable graph with minimum size is isomorphi...
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A graph G is called (H; k)-vertex stable if G contains a subgraph isomorphic to H ever after removing any k of its vertices; stab(H; k) denotes the minimum size among the sizes of all (H; k)-vertex stable graphs. In this paper we deal with (Cn; k)vertex stable graphs with minimum size. For each n we prove that stab(Cn; 1) is one of only two possible values and we give the exact value for infini...
متن کاملOn (Kq;k)-Stable Graphs
A graph G is called (H; k)-vertex stable if G contains a subgraph isomorphic to H even after removing any k of its vertices. By stab(H; k) we denote the minimum size among the sizes of all (H; k)-vertex stable graphs. Given an integer q ≥ 2, we prove that, apart of some small values of k, stab(Kq; k) = (2q−3)(k+1). This confirms in the affirmative the conjecture of Dudek et al. [(H, k) stable g...
متن کاملOn minimum (Kq, k) stable graphs
A graph G is a (Kq , k) vertex stable graph (q ≥ 3) if it contains a Kq after deleting any subset of k vertices (k ≥ 0). We are interested by the (Kq , κ(q)) vertex stable graphs of minimum size where κ(q) is the maximum value for which for every nonnegative integer k < κ(q) the only (Kq , k) vertex stable graph of minimum size is Kq+k.
متن کامل(H, k) stable graphs with minimum size
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(C3, k), Q(C4, k), Q(K1,p, k) and Q(Ks, k).
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2435