EXISTENCE OF X-PATHS IN ABSTRACT POLYTOPES

Abstract

Given a finite set E of n symbols a family S of subsets of E (called vertices) form an abstract polytope if (1) Each vertex is a subset of m symbols of E. (2) Every subset of m + 1 symbols of E contains either zero or two vertices (called adjacent). (3) Every pair of vertices V sup 0 and V sup * can be joined by a path V sup 0 = V sub 1, ..., V sub k = V sup * such that V sub i, V sub (i + 1) are adjacent and (V sub i) contained in (V sup 0) joined to (V sup *) i = 1, ..., k-1. It is shown that if two vertices of a given abstract polytope contain the same symbol (say x) then there exists a path such that every vertex along the path contains x.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1970
Accession Number
AD0706017

Entities

People

  • Geroge Dantzig
  • Ilan Adler
  • Katta Murty

Organizations

  • Stanford University

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Abstracts
  • Contracts
  • Engineering
  • Industrial Engineering
  • Michigan
  • Military Research
  • Nuclear Energy
  • Operations Research
  • Security
  • Systems Engineering
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.