On the Complexity of Arrangements of Circles in the Plane

@article{Alon2001OnTC,
  title={On the Complexity of Arrangements of Circles in the Plane},
  author={Noga Alon and Hagit Last and Rom Pinchasi and Micha Sharir},
  journal={Discrete & Computational Geometry},
  year={2001},
  volume={26},
  pages={465-492}
}
Continuing and extending the analysis in a previous paper [14], we establish several combinatorial results on the complexity of arrangements of circles in the plane. The main results are a collection of partial solutions to the conjecture that (a) any arrangement of unit circles with at least one intersecting pair has a vertex incident to at most 3 circles, and (b) any arrangement of circles of arbitrary radii with at least one intersecting pair has a vertex incident to at most 3 circles, under… CONTINUE READING