Dominating cliques in chordal graphs
نویسندگان
چکیده
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 ...
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In Hell et al. (2004), we have previously observed that, in a chordal graph G, the maximum number of independent r -cliques (i.e., of vertex disjoint subgraphs of G, each isomorphic to Kr , with no edges joining any two of the subgraphs) equals the minimum number of cliques of G that meet all the r -cliques of G. When r = 1, this says that chordal graphs have independence number equal to the cl...
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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...
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We prove that the problem of nding two minimum dominating sets (connected dominating sets or vertex clique covers) with minimum intersection is linearly solvable in interval graphs. Furthermore, the problem of deciding whether or not there exist two disjoint minimum dominating sets (connected dominating sets or vertex clique covers) is shown to be NP-hard for chordal graphs.
متن کاملEnumerating minimal dominating sets in chordal bipartite graphs
We show that all minimal dominating sets of a chordal bipartite graph can be generated in incremental polynomial, hence output polynomial, time. Enumeration of minimal dominating sets in graphs is equivalent to enumeration of minimal transversals in hypergraphs. Whether the minimal transversals of a hypergraph can be enumerated in output polynomial time is a well-studied and challenging questio...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90118-x