Geodesic
Bipartite and Series-Parallel Graphs Without Planar Lombardi Drawings
Journal of Graph Algorithms and Applications, Tome 25 (2021) no. 1, pp. 549-562.

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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.
DOI : 10.7155/jgaa.00571
Keywords: Lombardi drawing, bipartite graphs, series-parallel graphs, nonplanarity 
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David Eppstein. Bipartite and Series-Parallel Graphs Without Planar Lombardi Drawings. Journal of Graph Algorithms and Applications, Tome 25 (2021) no. 1, pp. 549-562. doi : 10.7155/jgaa.00571. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00571/

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