Euclidean Constructibility in Graph-Minimization Problems
Euclidean Constructibility in Graph-Minimization Problems
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图最小化问题中的欧几里得可构造性
DOI：
10.1080/0025570x.1969.11975961
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发表时间：
1969
影响因子：
--
通讯作者：
Z. A. Melzak
中科院分区：
文献类型：
--
作者：
E. Cockayne;Z. A. Melzak
1. 令 b1, * * *, bN 为平面上任意不同点的集合。对于顶点 b1,...,bv 上的树 U，我们指的是由一些 (2) 闭合直线段 bibj 组成的任何集合，其属性是任何两个顶点都可以通过属于 U 的一系列线段以一种且仅一种方式连接。线段bibj称为U的分支，U的长度L(U)是其分支长度之和，{bi}是向顶点bi发送分支的所有顶点的集合，w(b,)是它们的数量。我们现在将问题表述为：
1. Let b1, * * *, bN be any set of distinct points in the plane. By a tree U on the vertices b1, , bv we mean any set consisting of some of the (2) closed straight segments bibj with the property that any two vertices can be joined by a sequence of segments belonging to U in one and only one way. A segment bibj is called a branch of U, the length L(U) of U is the sum of the lengths of its branches, {bi} is the set of all vertices sending branches to the vertex bi and w(b,) is their number. We now formulate the problem: