A report on stable graphs
نویسندگان
چکیده
منابع مشابه
On (Cn;k) Stable Graphs
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 α-Square-Stable Graphs
The stability number of a graph G, denoted by α(G), is the cardinality of a maximum stable set, and μ(G) is the cardinality of a maximum matching in G. If α(G) + μ(G) equals its order, then G is a König-Egerváry graph. We call G an α-square-stable graph if α(G) = α(G), where G denotes the second power of G. These graphs were first investigated by Randerath and Wolkmann, [18]. In this paper we o...
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 Survey on Simulating Stable Random Variables
In general case, Chambers et al. (1976) introduced the following algorithm for simulating any stable random variables $ X/sim(alpha, beta, gamma, delta) $ with four parameters. They use a nonlinear transformation of two independent uniform random variables for simulating an stable random variable... (to continue, click here)
متن کاملOn Stable Cutsets in Claw-Free Graphs and Planar Graphs
A stable cutset in a connected graph is a stable set whose deletion disconnects the graph. Let K4 and K1,3 (claw) denote the complete (bipartite) graph on 4 and 1+ 3 vertices. It is NP-complete to decide whether a line graph (hence a claw-free graph) with maximum degree five or a K4-free graph admits a stable cutset. Here we describe algorithms deciding in polynomial time whether a claw-free gr...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1973
ISSN: 0004-9735
DOI: 10.1017/s144678870001291x