Balanced partitions of two sets of points in the plane
Balanced partitions of two sets of points in the plane
复制标题
平面上两组点的平衡划分
DOI：
10.1016/s0925-7721(99)00024-3
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
M. Kano
中科院分区：
文献类型：
--
作者：
A. Kaneko;M. Kano
我们证明了下面的定理。设m≥2和q≥1是整数，S和T是平面上两个不相交的点集，使得S和T中没有三个点在同一直线上，|S| = 2 q和|不|=mq。则S ∈ T可以被划分为q个不相交的子集P1，P2，.，Pq，满足以下两个条件：（i）conv（Pi）conv（Pj）=φ，对于所有1≤i<j≤q，其中conv（Pi）表示Pi的船体;以及（ii）|派·斯|=2和|Pi∩T| =m，对于所有1≤i≤q。
We prove the following theorem. Let m≥2 and q≥1 be integers and let S and T be two disjoint sets of points in the plane such that no three points of S∪T are on the same line, |S|=2q and |T|=mq. Then S∪T can be partitioned into q disjoint subsets P1,P2,…,Pqsatisfying the following two conditions: (i) conv(Pi)∩conv(Pj)=φ for all 1≤i<j≤q, where conv(Pi) denotes the convex hull of Pi; and (ii) |Pi∩S|=2 and |Pi∩T|=m for all 1≤i≤q.