Year: 2012
Type: preprint
Abstract: We prove that every planar graph with maximum degree three has a planar drawing in which the edges are drawn as circular arcs that meet at equal angles around every vertex. Our construction is based on the Koebe-Thurston-Andreev circle packing theorem, and uses a novel type of Voronoi diagram for circle packings that is invariant under Moebius transformations, defined using three-dimensional hyperbolic geometry. We also use circle packing to construct planar Lombardi drawings of a special class of 4-regular planar graphs, the medial graphs of polyhedral graphs, and we show that not every 4-regular planar graph has a Lombardi drawing. We have implemented our algorithm for 3-connected planar cubic graphs.
Source: arXiv (Cornell University)
Author: Eppstein, David
Institution: University of California, Irvine
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950424295