Convex and Linear Orientations of Polytopal Graphs

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 functions that induce the given orientation. For each combinatorial class of 3-polytopes, we provide a good characterization of the orientations that are induced by an affine function acting on some member of the class.

• Type: Journal
• Year: 2000
• Where: DCG
• Authors: J. Mihalisin, Victor Klee
• Keywords: Acyclic Orientation, Combinatorial Class, Convex Polytopes, DCG 2000