Split Orders

In this paper, we study structural and algorithmic properties of split orders, that is of orders whose comparability graph is a split graph. We introduce a normalized representation of these orders, using a family of open real intervals, and having some interesting consequences. We show that the dimension of split orders is at most three, and we give a simple characterization of those of dimension two. We present two algorithms, a linear time one recognizing these directed graphs whose transitive closure is a split order, and a greedy one generating all split orders of a given size once up to isomorphism.