Path-driven orientation of mixed graphs

Path-driven orientation of mixed graphs

We consider in this paper two graph orientation problems. The input of both problems is (i) a mixed graph G whose vertex set is V and edge set (resp. arc set) is E (resp. A) and (ii) a set P ⊆ V × V of source-target pairs. The first problem, called S-GO, is a decision problem introduced by Hassin and Megiddo (Linear Algebra and its Applications 114 (1989): 589-602) and defined as follows: is it...

Unilateral Orientation of Mixed Graphs

A digraph D is unilateral if for every pair x, y of its vertices there exists a directed path from x to y, or a directed path from y to x, or both. A mixed graph M = (V,A,E) with arc-set A and edgeset E accepts a unilateral orientation, if its edges can be oriented so that the resulting digraph is unilateral. In this paper, we present the first linear-time recognition algorithm for unilaterally...

Forced Orientation of Graphs

forced orientation of graphs

From Path Graphs to Directed Path Graphs

We present a linear time algorithm to greedily orient the edges of a path graph model to obtain a directed path graph model (when possible). Moreover we extend this algorithm to find an odd sun when the method fails. This algorithm has several interesting consequences concerning the relationship between path graphs and directed path graphs. One is that for a directed path graph, path graph mode...