Convex drawings of graphs in two and three dimensions (preliminary version)
Proceedings of the twelfth annual symposium on Computational geometry
Handbook of discrete and computational geometry
Drawing Stressed Planar Graphs in Three Dimensions
GD '95 Proceedings of the Symposium on Graph Drawing
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We introduce a new wider class of polyhedra called upward (star-shaped) polyhedra, and present a graph-theoretic characterization. Our proof includes a drawing algorithm which constructs an upward polyhedron with n vertices in O(n 1.5) time. Moreover, we can test whether a given plane graph is an upward polyhedral graph in linear time. Our result is the first graph-theoretic characterization of non-convex polyhedra, which solves an open problem posed by Grünbaum [6], and a generalization of the Steinitz' theorem [9].