Showing papers on "K-tree published in 1971"
01 Sep 1971
TL;DR: In this article, a general and convenient framework for investigating the combinatorial structure of simple polytopes is given by a set of three axioms (proposed by G. B. Dantzig) which define abstract polytope.
Abstract: : A general and convenient framework for investigating the combinatorial structure of simple polytopes is given by a set of three axioms (proposed by G. B. Dantzig) which define abstract polytopes. These axioms are discussed and it is shown that, combinatorially, simple polytopes constitute a proper subclass of abstract polytopes. The purpose of the paper is to study the graphs and dual graphs of abstract polytopes and in particular, to show that some well-known properties of graphs of polytopes are satisfied also by the graphs and dual graphs of abstract polytopes.
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