Lombardi drawings of knots and links

In Lombardi drawings of graphs, edges are represented as circular arcs and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing and not every planar graph has a planar Lombardi drawing. We introduce k-Lombardi drawings, in which each edge may be drawn with k circular arcs; we show that every graph has a smooth 2-Lombardi drawing and every planar graph has a smooth planar 3-Lombardi drawing. We also investigate related topics connecting planarity and Lombardi drawings.

keywords: Computational Geometry, Graph Drawing, Graphs Theory

Conference Proceedings (peer-reviewed)

André Schulz, Birgit Vogtenhuber, Dylan Thurston, Maarten Löffler, Martin Nöllenburg, Philipp Kindermann, Stephen Kobourov
Lombardi drawings of knots and links
Proc. 25th Symposium on Graph Drawing
(to appear), 2017

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