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arXiv · 2212.02668

On finding hamiltonian cycles in Barnette graphs

Behrooz Bagheri Gh.·Tomas Feder·Herbert Fleischner·Carlos Subi
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Abstract

In this paper, we deal with hamiltonicity in planar cubic graphs G having a facial 2-factor Q via (quasi) spanning trees of faces in G/Q and study the algorithmic complexity of finding such (quasi) spanning trees of faces. Moreover, we show that if Barnette's Conjecture is false, then hamiltonicity in 3-connected planar cubic bipartite graphs is an NP-complete problem.

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Behrooz Bagheri Gh., Tomas Feder, Herbert Fleischner, Carlos Subi. 2022-12-13. On finding hamiltonian cycles in Barnette graphs. https://arxiv.org/abs/2212.02668

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