JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Abstract. We prove that the edge dominating set problem for graphs is NP-complete even when restricted to planar or bipartite graphs of maximum degree 3. We show as a corollary that the minimum maximal matching and the achromatic number problems are NP-complete. A new linear time algorithm for finding minimum independent edge dominating sets in trees is described, based on an observed relationship between edge dominating sets and independent sets in total graphs. Society for Industrial and Applied Mathematics
Yannakakis and Gavril REF proved that the edge dominating set problem is NP-hard even in planar or bipartite graphs of maximum degree 3.
Edge Dominating Sets in Graphs
Siam Journal on Applied Mathematics
Mathematics