On RAC Drawings of Graphs with Two Bends per Edge
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916465185128448 |
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| author | Tóth, Csaba D. |
| author_facet | Tóth, Csaba D. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_02663 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On RAC Drawings of Graphs with Two Bends per Edge Tóth, Csaba D. Discrete Mathematics Computational Geometry 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. |
| title | On RAC Drawings of Graphs with Two Bends per Edge |
| topic | Discrete Mathematics Computational Geometry |
| url | https://arxiv.org/abs/2308.02663 |