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On finding hamiltonian cycles in Barnette graphs
Behrooz Bagheri Gh., Tomas Feder, Herbert Fleischner, Carlos Sub · 2022-12-06 · via math.CO updates on arXiv.org

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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