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.

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Paul Hunter, Stephan Kreutzer
• Keywords: Elimination Orderings, Equivalent Complexity Measures, Natural Connectivity Measure, TCS 2008, Theoretical Computer Science