Abstract
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].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
