Abstract
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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Duncan, C.A., Eppstein, D., Goodrich, M.T., Kobourov, S.G., Löffler, M. (2012). Planar and Poly-arc Lombardi Drawings. In: van Kreveld, M., Speckmann, B. (eds) Graph Drawing. GD 2011. Lecture Notes in Computer Science, vol 7034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25878-7_30
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DOI: https://doi.org/10.1007/978-3-642-25878-7_30
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