Bipartite and series-parallel graphs without planar Lombardi drawings.
D. Eppstein.
arXiv:1906.04401.
Proc. 31st Canadian Conference on
Computational Geometry, Edmonton, Canada, 2019, pp. 17–22.
J. Graph Algorithms &
Applications 25 (1): 549–562, 2021, doi:10.7155/jgaa.00571.
Not every bipartite planar graph has a planar Lombardi drawing. Not every plane series parallel graph has a planar Lombardi drawing with the same embedding. The proof involves the properties of cycles of circular-arc-quadrilaterals all sharing the same two vertices, with equal and sharp vertex angles.