Planar and Poly-Arc Lombardi Drawings

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.


slides
keywords: Computational Geometry, Graph Drawing, Graphs Theory

Conference Proceedings (peer-reviewed)

Christian Duncan, David Eppstein, Maarten Löffler, Michael T. Goodrich, Stephen Kobourov
Planar and Poly-Arc Lombardi Drawings
Proc. 19th Symposium on Graph Drawing
LNCS, 7034, 308–319, 2011
http://dx.doi.org/10.1007/978-3-642-25878-7_30

Archived Publication (not reviewed)

Christian Duncan, David Eppstein, Maarten Löffler, Michael T. Goodrich, Stephen Kobourov
Planar and Poly-Arc Lopmbardi Drawings
1109.0345, 2011
http://arXiv.org/abs/1109.0345

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