TY - JOUR

T1 - On the complexity of arrangements of circles in the plane

AU - Alon, N.

AU - Last, H.

AU - Pinchasi, R.

AU - Sharir, M.

PY - 2001/12

Y1 - 2001/12

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=0035623196&partnerID=8YFLogxK

U2 - 10.1007/s00454-001-0043-x

DO - 10.1007/s00454-001-0043-x

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0035623196

SN - 0179-5376

VL - 26

SP - 465

EP - 492

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 4

ER -