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
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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 -