Continuing and extending the analysis in a previous paper , 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 three circles, and (b) any arrangement of circles of arbitrary radii with at least one intersecting pair has a vertex incident to at most three circles, under appropriate assumptions on the number of intersecting pairs of circles (see below for a more precise statement).
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics