Algorithmic aspects of upper edge domination

We study the problem of finding a minimal edge dominating set maximum size in given graph G=(V,E), called Upper EDS. show that this is not approximable within ratio nε−12, for any ε∈(0,12), assuming P≠NP, where n=|V|. On other hand, graphs minimum degree at least 2, we give an approximation algorithm with 1n, matching lower bound. further EDS APX-complete bipartite 4, and NP-hard planar 4.