A Sufficient Condition for Cubic 3‐Connected Plane Bipartite Graphs to be Hamiltonian

ABSTRACT Barnette's conjecture asserts that every cubic 3‐connected plane bipartite graph is hamiltonian. Although, in general, the problem is still open, some partial results are known. In particular, let us call a face of a plane graph big (small) if it has at least six edges (it has four edges, respectively). Goodey proved for a 3‐connected bipartite cubic plane graph , that if all big faces in have exactly six edges, then is hamiltonian. In this paper, we prove that the same is true under the condition that no face in has more than four big neighbours. We also prove, that if each vertex in is incident both with a small and a big face, then has at least different Hamilton cycles, where , is the number of big faces in and is the maximum size of faces in .