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Directed Tree-Width Examples Isolde Adler

Summary: Directed Tree-Width Examples
Isolde Adler
Mathematisches Institut,
Eckerstr. 1,
D-79102 Freiburg
5th June 2005
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
from [1]1. Let D be a digraph. A set S D \ Z is Z-normal, if there is no
directed walk in D\Z with first and last vertex in S that uses a vertex from D\


Source: Adler, Isolde - Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt am Main


Collections: Computer Technologies and Information Sciences