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Edge Dominating Sets in Graphs

M. Yannakakis and F. Gavril
SIAM Journal on Applied Mathematics
Vol. 38, No. 3 (Jun., 1980), pp. 364-372
Stable URL: http://www.jstor.org/stable/2100648
Page Count: 9
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Edge Dominating Sets in Graphs
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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.

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