The Mani-Walkup Spherical Counterexamples to the Wv-Path Conjecture are Not Polytopal
Published Online:1 Feb 1985https://doi.org/10.1287/moor.10.1.158
Abstract
Mani and Walkup (Mani, P., D. W. Walkup. 1980. A 3-sphere counterexample to the Wv-path conjecture. Math. Oper. Res.5 595–598.) described two triangulated 3-spheres which give rise to “small” counterexamples to the Wv-path and Hirsch conjectures for spheres. We show that none of these spheres is combinatorially equivalent to any 4-polytope. Thus the Wv-path and Hirsch conjectures for polytopes are still open.
