Planar and Poly-arc Lombardi Drawings
Duncan, Christian A. and Eppstein, David and Goodrich, Michael T. and Kobourov, Stephen G. and Löffler, Maarten (2012) Planar and Poly-arc Lombardi Drawings. In: Graph Drawing 19th International Symposium, GD 2011, September 21-23, 2011, Eindhoven, The Netherlands , pp. 308-319 (Official URL: http://dx.doi.org/ 10.1007/978-3-642-25878-7_30).
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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, noting that every graph has a smooth 2-Lombardi drawing. We show that every planar graph has a smooth planar 3-Lombardi drawing and further investigate topics connecting planarity and Lombardi drawings.
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