A Study on f Number of Points for Number of Points with Inter-Distance of Less Than, or for Number of Points with Inter-Distance of or More to Necessarily Exist on Plane
We defined number of points with an inter-distance of β or more to necessarily exist on a plane. Furthermore, we aimed to reduce the range of this minimum value. We first showed that the upper bound of this value could be scaled by , and further reduced the constant that was multiplied. We compared the upper bound of and the Ramsey number in a special case and confirmed that was a better upper bound than except when were both small or trivial.
2004 ◽
Vol 41
(4)
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pp. 1081-1092
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2009 ◽
Vol 20
(02)
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pp. 313-329
1994 ◽
Vol 3
(4)
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pp. 429-434
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2021 ◽
Vol 0
(0)
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pp. 0
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