Algorithmic aspects of upper edge domination

Abstract

We study the problem of finding a minimal edge dominating set of maximum size in a given graph G=(V,E), called UPPER EDS. We show that this problem is not approximable within a ratio of [Formula presented], for any [Formula presented], assuming P≠NP, where n=|V|. On the other hand, for graphs of minimum degree at least 2, we give an approximation algorithm with ratio [Formula presented], matching this lower bound. We further show that UPPER EDS is APX-complete in bipartite graphs of maximum degree 4, and NP-hard in planar bipartite graphs of maximum degree 4.