A sufficient condition for cubic 3-connected plane bipartite graphs to be hamiltonian

Jan Florek

Sep 2023

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摘要原文

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 if it has at least six edges. Goodey proved for a 3-connected bipartite cubic plane graph P, that if all big faces in P have exactly six adges, then P is hamiltonian. In this paper we prove that the same is true under the condition that no face in P has more than four big neighbours. 15 pages

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