English

Bipartite and Series-Parallel Graphs Without Planar Lombardi Drawings

Computational Geometry 2021-12-10 v2

Abstract

We find a family of planar bipartite graphs all of whose Lombardi drawings (drawings with circular arcs for edges, meeting at equal angles at the vertices) are nonplanar. We also find families of embedded series-parallel graphs and apex-trees (graphs formed by adding one vertex to a tree) for which there is no planar Lombardi drawing consistent with the given embedding.

Keywords

Cite

@article{arxiv.1906.04401,
  title  = {Bipartite and Series-Parallel Graphs Without Planar Lombardi Drawings},
  author = {David Eppstein},
  journal= {arXiv preprint arXiv:1906.04401},
  year   = {2021}
}

Comments

10 pages, 6 figures. A preliminary version of this paper appeared at the 31st Canadian Conference in Computational Geometry

R2 v1 2026-06-23T09:49:46.321Z