No abstract

An edge dominating set of a graph G = (V, E) is a subset M ⊆ E of edges such that each edge in E \ M is incident to at least one edge in M. In this paper, we consider the parameterized edge dominating set problem which asks us to test whether a given graph has an edge dominating set with size bounded from above by an integer k or not, and we design an O * (2.2351 k)-time and polynomialspace algorithm. This is an improvement over the previous best time bound of O * (2.3147 k). We also show that a related problem: the parameterized weighted edge dominating set problem can be solved in O * (2.2351 k) time and polynomial space.

SUMMARYGiven an undirected graph G, an edge dominating set is a subset F of edges such that each edge not in F is adjacent to some edge in F, and computing the minimum size of an edge dominating set is known to be NP-hard. Since the size of any edge dominating set is at least half of the maximum size μ(G) of a matching in G, we study the problem of testing whether a given graph G has an edge dominating set of size μ(G)/2 or not. In this paper, we prove that the problem is NP-complete, whereas we design an O * (2.0801 μ(G)/2 )-time and polynomial-space algorithm to the problem.