Bipartite and Series-Parallel Graphs Without Planar Lombardi Drawings
Vol. 25, no. 1, pp. 549-562, 2021. Regular paper.
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.

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Submitted: April 2021.
Reviewed: September 2021.
Revised: September 2021.
Accepted: October 2021.
Final: October 2021.
Published: October 2021.
Communicated by Ignaz Rutter
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