Optimal Bounds on Constrained Theta-Graphs

André van Renssen

We present tight upper and lower bounds on the spanning ratio of a large family of constrained θ-graphs. We show that constrained θ-graphs with 4k+2 cones (k≥1 and integer) have a spanning ratio of 1+2sin(θ/2), where θ is 2π/(4k+2).