On the complexity of arrangements of circles in the plane

N. Alon*, H. Last, R. Pinchasi, M. Sharir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)465-492
Number of pages28
JournalDiscrete and Computational Geometry
Volume26
Issue number4
DOIs
StatePublished - Dec 2001

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