科研之友
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摘要
Let P be a set of n blue points in the plane, not all on a line. Let R be a set of m red points such that P boolean AND R = 0 and every line determined by P contains a point from R. We provide an answer to an old problem by Grunbaum and Motzkin [9] and independently by Erdos and Purdy [6] who asked how large must m be in terms of n in such a case? More specifically, both [9] and [6] were looking for the best absolute constant c such that m %26gt;= cn. We provide an answer to this problem and show that m %26gt;= (n - 1)/3.
- 出版日期2013-11
