1 research outputs found
An time algorithm for minimum weighted dominating induced matching
Say that an edge of a graph dominates itself and every other edge
adjacent to it. An edge dominating set of a graph is a subset of
edges which dominates all edges of . In particular, if
every edge of is dominated by exactly one edge of then is a
dominating induced matching. It is known that not every graph admits a
dominating induced matching, while the problem to decide if it does admit it is
NP-complete. In this paper we consider the problems of finding a minimum
weighted dominating induced matching, if any, and counting the number of
dominating induced matchings of a graph with weighted edges. We describe an
exact algorithm for general graphs that runs in time and
polynomial (linear) space. This improves over any existing exact algorithm for
the problems in consideration.Comment: 17 page