Digraph measures: Kelly decompositions, games, and orderings

Paul Hunter, Stephan Kreutzer
2008 Theoretical Computer Science  
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 the translations of 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 potential
more » ... lications 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.
doi:10.1016/j.tcs.2008.02.038 fatcat:kmiscfo3kvafflb4o66nswgyxa