Digraph measures: Kelly decompositions, games, and orderings

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Digraph measures: Kelly decompositions, games, and orderings
We consider various well-known, equivalent complexity measures for graphs such as elimination orderings, k-trees and cops and robber games and study their natural translations to digraphs. We show that on digraphs all these measures are also equivalent and induce a natural connectivity measure. We introduce a decomposition for digraphs and an associated width, Kelly-width, which is equivalent to the aforementioned measure. We demonstrate its usefulness by exhibiting a number of potential applications including polynomial-time algorithms for NP-complete problems on graphs of bounded Kelly-width, and complexity analysis of asymmetric matrix factorization. Finally, we compare the new width to other known decompositions of digraphs.
Paul Hunter, Stephan Kreutzer
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TCS
Authors Paul Hunter, Stephan Kreutzer
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