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arXiv · 2308.02663

On RAC Drawings of Graphs with Two Bends per Edge

Csaba D. Tóth
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Abstract

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 $n\geq 3$. 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.

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Csaba D. Tóth. 2023-08-04. On RAC Drawings of Graphs with Two Bends per Edge. https://doi.org/10.7155/jgaa.v28i2.2939

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