We show that, unlike the Yao–Yao graph YY6, the Theta–Theta graph ΘΘ6 defined by six cones is a spanner for sets of points in convex position. We also show that, for sets of points in non-convex position, the spanning ratio of ΘΘ6 is unbounded.
Damian, M., Iacono, J. & Winslow, A. Spanning Properties of Theta–Theta-6. Graphs and Combinatorics 36, 525–538 (2020). https://doi.org/10.1007/s00373-020-02135-2
Graphs and Combinatorics