Upper bounds on the spanning ratio of constrained theta-graphs
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 4k2 (k≥ 1 and integer) cones have a tight spanning ratio of 1+2 sin(θ/2), where θ is 2 π/ (4k+2). We also present improved upper bounds on the spanning ratio of the other families of constrained θ-graphs.
Bose, P, & Van Renssen, A. (André). (2014). Upper bounds on the spanning ratio of constrained theta-graphs. doi:10.1007/978-3-642-54423-1_10