Edge dominating sets and vertex covers
نویسندگان
چکیده
منابع مشابه
Edge dominating sets and vertex covers
Bipartite graphs with equal edge domination number and maximum matching cardinality are characterized. These two parameters are used to develop bounds on the vertex cover and total vertex cover numbers of graphs and a resulting chain of vertex covering, edge domination, and matching parameters is explored. In addition, the total vertex cover number is compared to the total domination number of ...
متن کاملVertex covers by edge disjoint
Let H be a simple graph having no isolated vertices. An (H; k)-vertex-cover of a simple graph G = (V;E) is a collection H1; : : : ;Hr of subgraphs of G satisfying 1. Hi = H; for all i = 1; : : : ; r; 2. [i=1V (Hi) = V , 3. E(Hi) \ E(Hj) = ;; for all i 6= j; and 4. each v 2 V is in at most k of the Hi. We consider the existence of such vertex covers when H is a complete graph, Kt; t 3, in the co...
متن کاملEfficient Dominating and Edge Dominating Sets for Graphs and Hypergraphs
Let G = (V,E) be a graph. A vertex dominates itself and all its neighbors, i.e., every vertex v ∈ V dominates its closed neighborhood N [v]. A vertex set D in G is an efficient dominating (e.d.) set for G if for every vertex v ∈ V , there is exactly one d ∈ D dominating v. An edge set M ⊆ E is an efficient edge dominating (e.e.d.) set for G if it is an efficient dominating set in the line graph...
متن کاملTropical Dominating Sets in Vertex-Coloured Graphs
Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various param...
متن کاملSmall Edge Dominating Sets of Regular Graphs
An edge dominating set F of a graph G is a subset of E(G) such that every edge in E(G) \ F is incident with at least one vertex that is an end-point of an edge in F . Edge dominating sets of small cardinality are of interest. We refer to the size of a smallest edge dominating set of a graph G as the edge domination number of G and denote this by β(G). In this paper we improve all current known ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2013
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1681