Arrangements of n Points whose Incident-Line-Numbers are at most n/2 |
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Authors: | Jin Akiyama Hiro Ito Midori Kobayashi Gisaku Nakamura |
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Affiliation: | (2) Department of Computer Science, Lund University, Lund, Sweden |
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Abstract: | We consider a set X of n noncollinear points in the Euclidean plane, and the set of lines spanned by X, where n is an integer with n ≥ 3. Let t(X) be the maximum number of lines incident with a point of X. We consider the problem of finding a set X of n noncollinear points in the Euclidean plane with t(X) £ ?n/2 ?{t(X) le lfloor n/2 rfloor}, for every integer n ≥ 8. In this paper, we settle the problem for every integer n except n = 12k + 11 (k ≥ 4). The latter case remains open. |
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