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Bipartite and Series-Parallel Graphs Without Planar Lombardi Drawings (1906.04401v2)
Published 11 Jun 2019 in cs.CG
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.