Planar and Poly-Arc Lombardi Drawings
Computational Geometry
2018-09-10 v1 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.1109.0345,
title = {Planar and Poly-Arc Lombardi Drawings},
author = {Christian A. Duncan and David Eppstein and Michael T. Goodrich and Stephen G. Kobourov and Maarten Löffler},
journal= {arXiv preprint arXiv:1109.0345},
year = {2018}
}
Comments
Expanded version of paper appearing in the 19th International Symposium on Graph Drawing (GD 2011). 16 pages, 8 figures