Hamiltonian circuits on simple 3-polytopes with up to 30 vertices
Haruko Okamura · Journal of the Mathematical Society of Japan · 1982
\S 1. Introduction.Klee in [5] asked what is the minimun number, $n$ , of vertices for a simple 3-polytope with no Hamiltonian circuit, that is, no closed path on the edges of the polytope which goes through each vertex exactly once.The smallest known non-Hamiltonian simple 3-polytope has 38 vertices (see p. 359 in [5]), so $n\leqq 38$ .Lederberg [6] proved $n\geqq 20$ , Butler [2] and Goodey [4] proved $n\geqq 24$ , Barnette