Are all simple 4-polytopes Hamiltonian?
A conjecture of D. Barnette says that all simple 4-polytopes are Hamiltonian. The author constructs a large family of non-Hamiltonian 4- connected 4-regular graphs, and proves all of them to be non-polytopal by showing that they may not be the dual graphs of triangulations of the 3- sphere.
scientific article; zbMATH DE number 3855154