Accession Number:

AD0706017

Title:

EXISTENCE OF X-PATHS IN ABSTRACT POLYTOPES

Descriptive Note:

Technical rept.

Corporate Author:

STANFORD UNIV CA OPERATIONS RESEARCH HOUSE

Report Date:

1970-03-01

Pagination or Media Count:

8.0

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.

Subject Categories:

  • Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE