EXISTENCE OF X-PATHS IN ABSTRACT POLYTOPES
STANFORD UNIV CA OPERATIONS RESEARCH HOUSE
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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.
- Operations Research