Abstract.
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.
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Received March 10, 1999, and in revised form May 30, 1999. Online publication May 16, 2000.
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Mihalisin, J., Klee, V. Convex and Linear Orientations of Polytopal Graphs . Discrete Comput Geom 24, 421–436 (2000). https://doi.org/10.1007/s004540010046
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DOI: https://doi.org/10.1007/s004540010046