Abstract
We extend the concept of rectangular drawing to drawings on a sphere using meridians and circles of latitude such that each face is bounded by at most two circles and at most two meridians. This is called spherical-rectangular drawing. Special cases include drawing on a cylinder, a cone, or a lattice of concentric circles on the plane. In this paper, we prove necessary and sufficient conditions for cubic planar graphs to have spherical-rectangular drawings, and show that one can find in linear time a spherical-rectangular drawing of a subcubic planar graph if it has one.
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Hasheminezhad, M., Hashemi, S.M., McKay, B.D. (2009). Spherical-Rectangular Drawings. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_30
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DOI: https://doi.org/10.1007/978-3-642-00202-1_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00201-4
Online ISBN: 978-3-642-00202-1
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