Weak-order extensions of an order
In this paper, at first we describe a digraph representing all the weak-order extensions of a partially ordered set and algorithms for generating them. Then we present a digraph representing all of the minimal weak-order extensions of a partially. ordered set. This digraph also implies generation algorithms. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability invariant, whereas. the number of minimal weak-order extensions of a partially ordered set is not a comparability invariant. (C) 2003 Elsevier B.V. All rights reserved.
weak-order extension of an order partial order algorithm graph complexity