Abstract
A path in a polytope is called a W v path provided it never returns to any facet once it leaves it (Theorem 1). If x and y are two vertices of a 3-dimensional convex polytope then x and y can be joined by a W v path. If x and y do not lie on a common edge then they can be joined by two independent W v paths, and it they do not lie on a common facet then they can be joined by three independent W v paths. Results are obtained dealing with the question “when is a shortest path a W v path?” Also using ideas related to W v paths it is shown that any two vertices of a polytope with n k-dimensional faces can be joined by a path of length at most (3 k−3 ) n
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