Planar and Poly-Arc Lombardi Drawings

Details Planar and Poly-Arc Lombardi Drawings Planar and Poly-Arc Lombardi Drawings

2011-09-02

arxiv.org/abs/1109.0345v1

Computer Science

Computational Geometry

Expanded version of paper appearing in the 19th International Symposium on Graph Drawing (GD 2011). 16 pages, 8 figures

Scientific paper

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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