English

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

R2 v1 2026-06-21T18:58:41.570Z