Improved Bounds on the Spanning Ratio of the Theta-5-Graph - Bose, Prosenjit; Hill, Darryl; Ooms, Aurélien (Algorithms and Data Structures, 2021)
We show an upper bound of sin3π10sin2π5-sin3π10<5.70 $$ \frac{\sin \left( \frac{3π }{10}\right) }{\sin \left( \frac{2π }{5}\right) -\sin \left( \frac{3π }{10}\right) } <5.70$$ on the spanning ratio of Θ5 $$\varTheta _5$$ -graphs, improving on the previous best known upper bound of 9.96 $$9.96$$ [Bose, Morin, van Renssen, and Verdonschot. The Theta-5-graph is a spanner. Computational Geometry, 2015.]