For an acyclic directed graph with multiple sources and multiple sinks, we prove that one can choose the Menger's paths between the sources and the sinks such that the number...
Unique-sink orientations (USOs) are an abstract class of orientations of the ncube graph. We consider some classes of USOs that are of interest in connection with the linear compl...
Suppose that D is an acyclic orientation of the graph G. An arc of D is dependent if its reversal creates a directed cycle. Let d(D) denote the number of dependent arcs in D. Defi...
This paper examines directed graphs related to convex polytopes. For each fixed d-polytope and any acyclic orientation of its graph, we prove there exist both convex and concave fu...