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, Mirela; Iacono, John; and Winslow, Andrew, "Spanning Properties of Theta-Theta-6" (2020). Computer Science Faculty Publications and Presentations. 20.
Graphs and Combinatorics