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Register a new userCharacterizing Graphs of Zonohedra
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Added by
Masud Hasan
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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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.
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This is the arXiv index for the electronic proceedings of GD 2019, which contains the peer-reviewed and revised accepted papers with an optional appendix. Proceedings (without appendices) are also to be published by Springer in the Lecture Notes in Computer Science series.
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