Paths on Polytopes
Paths on Polytopes
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多面体上的路径
DOI：
10.1112/plms/s3-20.1.161
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发表时间：
1970
影响因子：
1.8
通讯作者：
D. Larman
中科院分区：
文献类型：
--
作者：
D. Larman
本文主要研究了线性规划的有界<#-步猜想及其相关的连通胞腔复形上T^-路的存在性问题。然而，也给出了关于具有给定顶点数或面数的三维多面体的半径的一些结果。但首先一些定义。拓扑多面体。在Rfc中，多面体P是有限个点的凸船体; P是^维的，如果它包含一个内点。Rfc中的拓扑多面体C是多面体P在同胚< D下的像，赋予其由O从P的面结构诱导的面结构。^维拓扑多面体C的（k-1）维面称为C的刻面。
This paper is primarily concerned with contributions to the long-standing bounded<#-step conjecture of linear programming and the associated problem of the existence of T^-paths on connected cell complexes. However, some results concerning the radius of three-dimensional polytopes with a given number of vertices or facets are also given. But first some definitions.Topological poly tope. In Rfc a poly tope P is the convex hull of a finite number of points; P is^-dimensional if it contains an interior point. A topological polytope C in Rfc is the image of a polytope P under a homeomorphism< D, endowed with the facial structure induced on it by O from the facial structure of P. The (k—1)-dimensional faces of a^-dimensional topological polytope C are called the facets of C.