Digraph Decompositions and Monotonicity in Digraph Searching

  • Authors:

  • Stephan Kreutzer;Sebastian Ordyniak

  • Affiliations:

  • Oxford University Computing Laboratory,;Oxford University Computing Laboratory,

  • Venue:
  • Graph-Theoretic Concepts in Computer Science
  • Year:
  • 2008

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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.