Directed tree-width examples

In [1] Johnson, Robertson, Seymour and Thomas define the notion of directed tree-width dtw(D) of a directed graph D. They ask whether dtw(D) ≥ k − 1 implies that D has a haven of order k. A negative answer is given. Furthermore they define a generalisation of the robber and cops game of [3] to digraphs. They ask whether it is true that if k cops can catch the robber on a digraph, then they can do so robber-monotonely. Again a negative answer is given. We also show that contraction of butterfly edges can increase directed tree-width. 1 Definitions All graphs and digraphs are finite. We recall the most important definitions

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Isolde Adler
• Keywords: Directed Graph D, JCT 2007, Negative Answer, Tree-width