NOTE ON THE NUMBER OF OBTUSE ANGLES IN POINT SETS
2014 ◽
Vol 24
(03)
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pp. 177-181
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In 1979 Conway, Croft, Erdős and Guy proved that every set S of n points in general position in the plane determines at least [Formula: see text] obtuse angles and also presented a special set of n points to show the upper bound [Formula: see text] on the minimum number of obtuse angles among all sets S. We prove that every set S of n points in convex position determines at least [Formula: see text] obtuse angles, hence matching the upper bound (up to sub-cubic terms) in this case. Also on the other side, for point sets with low rectilinear crossing number, the lower bound on the minimum number of obtuse angles is improved.
2020 ◽
Vol 29
(04)
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pp. 2050022
1997 ◽
Vol 6
(3)
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pp. 353-358
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2000 ◽
Vol 10
(01)
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pp. 73-78
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2015 ◽
Vol Vol. 17 no.2
(Graph Theory)
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2008 ◽
Vol Vol. 10 no. 3
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Keyword(s):
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2019 ◽
Vol 38
(5)
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pp. 197-204
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