Summary: Order 5 (1988), 33-43.
0 1988 by Kluwer Academic Publishers
On the Width of an Orientation of a Tree*
M. D. ATKINSON and D. T. H. NG
School ofComputer Science, Carleton University, Ottawa, Canada KlS 5B6
Communicated by I. Rival
(Received: 15 September 1987; accepted: 9 December 1987)
Abstract. There are 2"-t ways in which a tree on n vertices can be oriented. Each of these can
be regarded as the (Hasse) diagram of a partially ordered set. The maximal and minimal widths of
these posets are determined. The maximal width depends on the bipartition of the tree as a bipartite
graph and it can be determined in time O(n). The minimal width is one of LA/21 or IA/21 + 1, where
1 is the number of leaves of the tree. An algorithm of execution time O(n +A* log A) to construct
the minimal width orientation is given.
AMS subject classifications (1980). 06Al0,68(305.
Key words; Diagram, tree, orientation, width, algorithm.
Let T be any (unrooted) tree on n vertices. Each of the n - 1 edges of T can be
oriented in one of two directions and, hence, associated with T is a set of 2"-'
directed graphs. Each of these orientations of T can be regarded as the (Hasse)