Abstract
Continuing and extending the analysis in a previous paper [15], 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).
| Original language | English |
|---|---|
| Pages (from-to) | 465-492 |
| Number of pages | 28 |
| Journal | Discrete and Computational Geometry |
| Volume | 26 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1 Jan 2001 |
| Externally published | Yes |
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics