Abstract
We show an upper bound of \( \frac{\sin \left( \frac{3\pi }{10}\right) }{\sin \left( \frac{2\pi }{5}\right) -\sin \left( \frac{3\pi }{10}\right) } <5.70\) on the spanning ratio of \(\varTheta _5\)-graphs, improving on the previous best known upper bound of \(9.96\) [Bose, Morin, van Renssen, and Verdonschot. The Theta-5-graph is a spanner. Computational Geometry, 2015.]
Research supported in part by NSERC, VILLUM Foundation grant 16582, and FRIA Grant 5203818F (FNRS).
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- 1.
Angle values are given counter-clockwise unless otherwise stated.
- 2.
In what follows we use \(\triangle abc\) to denote the triangle defined by the points \(a\), \(b\), and \(c\) (given counter-clockwise). We use \(\angle abc\) to denote the amplitude of the angle at \(b\) in that triangle.
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Bose, P., Hill, D., Ooms, A. (2021). Improved Bounds on the Spanning Ratio of the Theta-5-Graph. In: Lubiw, A., Salavatipour, M., He, M. (eds) Algorithms and Data Structures. WADS 2021. Lecture Notes in Computer Science(), vol 12808. Springer, Cham. https://doi.org/10.1007/978-3-030-83508-8_16
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