The dag-width of directed graphs

@article{Berwanger2012TheDO,
  title={The dag-width of directed graphs},
  author={Dietmar Berwanger and Anuj Dawar and Paul Hunter and Stephan Kreutzer and Jan Obdrz{\'a}lek},
  journal={J. Comb. Theory, Ser. B},
  year={2012},
  volume={102},
  pages={900-923}
}
Tree-width is a well-known metric on undirected graphs thatmeasures how tree-like a graph is and gives a notion of graph decomposition that proves useful in algorithm development. Tree-width can be characterised by a graph searching game where a number of cops attempt to capture a robber. We consider the natural adaptation of this game to directed graphs and show that monotone strategies in the game yield a measure that can be seen to describe how close a directed graph is to a directed acyclic… CONTINUE READING

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