منابع مشابه
Dominating cliques in graphs
A set of vertices is a dominating set in a graph if every vertex not in the dominating set is adjacent to one or more vertices in the dominating set. A dominating clique is a dominating set that induces a complete subgraph. Forbidden subgraph conditions sufficient to imply the existence of a dominating clique are given. For certain classes of graphs, a polynomial algorithm is given for finding ...
متن کاملDominating Cliques in Distance-Hereditary Graphs
1 I n t r o d u c t i o n A subset D C V is a dominating set in graph G = (V, E) iff for all vertices v E V \ D there is a vertex u E D with uv E E. It is a dominating clique in G iff D is a dominating set in G and a clique (i.e. for all u, v E D uv E E). There are many papers investigating the problem of finding minimum dominating sets in graphs with (and without) additional requirements to th...
متن کاملr-Dominating cliques in graphs with hypertree structure
Let G = (V, E) be an undirected graph and r be a vertex weight function with positive integer values. A subset (clique) D ~_ V is an r-dominat ing set (clique) in G ifffor every vertex v e V there is a vertex u e D with dist(u, v) <~ r(v). This paper contains the following results: (i) We give a simple necessary and sufficient condition for the existence of r-dominating cliques in the case of H...
متن کاملOn Emergence of Dominating Cliques in Random Graphs
Emergence of dominating cliques in Erdös-Rényi random graph model G(n, p) is investigated in this paper. It is shown this phenomenon possesses a phase transition. Namely, we have argued that, given a constant probability p, an n-node random graph G from G(n, p) and for r = c log 1/p n with 1 ≤ c ≤ 2, it holds: (1) if p > 1/2 then an r-node clique is dominating in G almost surely and, (2) if p ≤...
متن کاملThreshold dominating cliques in random graphs and interval routing
The existence of (shortest-path) interval routing schemes for random graphs that use at most one interval label per edge is an open problem posed in [8]. In this paper, we show that for any random graph G(n, p) with edge probability p > 0.765, there exists an interval routing scheme that uses at most one label per edge and has an additive stretch 1. In doing so, we provide an interesting constr...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90353-j