• Corpus ID: 7950253

Towards Tight Bounds on Theta-Graphs

  title={Towards Tight Bounds on Theta-Graphs},
  author={Prosenjit Bose and Jean-Lou De Carufel and Pat Morin and Andr{\'e} van Renssen and Sander Verdonschot},
We present improved upper and lower bounds on the spanning ratio of $\theta$-graphs with at least six cones. Given a set of points in the plane, a $\theta$-graph partitions the plane around each vertex into $m$ disjoint cones, each having aperture $\theta=2\pi/m$, and adds an edge to the `closest' vertex in each cone. We show that for any integer $k \geq 1$, $\theta$-graphs with $4k+2$ cones have a spanning ratio of $1+2\sin(\theta/2)$ and we provide a matching lower bound, showing that this… 
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