Directed tree-width

We generalize thr concept of tree-width to directed graphs and prove that every directed graph with no "haven" of large order has small tree-width. Conversely, a digraph with a large haven has large tree-width. We also show that the Hamilton cycle problem and other NP-hard problems can be solved in polynomial time when restricted to digraphs of bounded tree-width. (C) 2001 Academic Press.