Characterizing Graphs of Zonohedra
Computational Geometry
2008-11-04 v1 Discrete Mathematics
Data Structures and Algorithms
Abstract
A classic theorem by Steinitz states that a graph G is realizable by a convex polyhedron if and only if G is 3-connected planar. Zonohedra are an important subclass of convex polyhedra having the property that the faces of a zonohedron are parallelograms and are in parallel pairs. In this paper we give characterization of graphs of zonohedra. We also give a linear time algorithm to recognize such a graph. In our quest for finding the algorithm, we prove that in a zonohedron P both the number of zones and the number of faces in each zone is O(square root{n}), where n is the number of vertices of P.
Cite
@article{arxiv.0811.0254,
title = {Characterizing Graphs of Zonohedra},
author = {Muhammad Abdullah Adnan and Masud Hasan},
journal= {arXiv preprint arXiv:0811.0254},
year = {2008}
}
Comments
13 pages, 5 figures