On minimum (Kq, k) stable graphs
نویسندگان
چکیده
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.
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...
متن کاملOn (Kq, k) vertex stable graphs with minimum size
A graph G is a (Kq, k) vertex stable graph if it contains a Kq after deleting any subset of k vertices. We give a characterization of (Kq, k) vertex stable graphs with minimum size for q = 3, 4, 5.
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 کاملA generalization of an independent set with application to (Kp;k)-stable graphs
We introduce a natural generalization of an independent set of a graph and give a sharp lower bound on its size. The bound generalizes the widely known Caro and Wei result on the independence number of a graph. We use this result in the following problem. Given nonnegative real numbers α, β the cost c(G) of a graph G is defined by c(G) = α|V (G)|+β|E(G)|. We estimate the minimum cost of a (Kq; ...
متن کاملMinimum cycle bases for direct products of K2 with complete graphs
We construct a minimum cycle basis for the direct product K2 × Kp of two complete graphs where p ≥ 2. For p > 3, these bases consists only of squares. This completes the work of R. Hammack, who treated the case Kp ×Kq for p, q ≥ 3 [Inform. Process. Lett. 102 (2007), 214–218.]
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 33 شماره
صفحات -
تاریخ انتشار 2013