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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
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2100648
Page Count: 9
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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.
SIAM Journal on Applied Mathematics © 1980 Society for Industrial and Applied Mathematics