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SIAM Journal on Applied Mathematics
Article
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Article . 1980
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SIAM Journal on Applied Mathematics
Article . 1980 . Peer-reviewed
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SIAM Journal on Applied Mathematics
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Edge Dominating Sets in Graphs

Edge dominating sets in graphs
descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1980 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Applied Mathematics, volume 38, pages 364-372 (issn: 0036-1399, eissn: 1095-712X, Copyright policy )
Authors: Mihalis Yannakakis; Fanica Gavril;

doi: 10.1137/0138030

Edge Dominating Sets in Graphs

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.

Related Organizations
Keywords

Coloring of graphs and hypergraphs, edge dominating sets, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), Graph theory (including graph drawing) in computer science, matching, linear time algorithm, Enumeration in graph theory, achromatic number, Trees, NP-complete

  • BIP!
    Impact byBIP!
    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 274
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 1%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
274
Top 1%
Top 1%
Average
bronze