On RAC Drawings of Graphs with Two Bends per Edge

08/04/2023

∙

by   Csaba D. Tóth, et al.

∙

0

∙

share

It is shown that every n-vertex graph that admits a 2-bend RAC drawing in the plane, where the edges are polylines with two bends per edge and any pair of edges can only cross at a right angle, has at most 20n-24 edges for n≥ 3. This improves upon the previous upper bound of 74.2n; this is the first improvement in more than 12 years. A crucial ingredient of the proof is an upper bound on the size of plane multigraphs with polyline edges in which the first and last segments are either parallel or orthogonal.