Digraph decompositions and monotonicity in digraph searching

Abstract

We consider graph searching games on directed graphs and corresponding digraph decompositions. In particular we show that two important variants of these games - underlying DAG- and Kelly-decompositions - are non-monotone. Furthermore, we explore the limits of algorithmic applicability of digraph decompositions and show that various natural candidates for problems, which potentially could benefit from digraphs having small "directed width", remain NP-complete even on almost acyclic graphs. © 2008 Springer Berlin Heidelberg.