Tait's conjecture on Hamiltonian planar cubic graphs
Let be a -regular, -connected planar graph. Tait's conjecture. Every such graph is Hamiltonian. The conjecture was disproved by W. T. Tutte, who constructed a counterexample on vertices; further counterexamples were found on vertices by Holton and McKay.
References
Primary source
Saptarshi Bej, “Hamiltonian cycles in annular decomposable Barnette graphs”, arXiv:2008.06671 (2020).
Additional references
3 papers in this index state this conjecture (2013–2020). The statement above is taken from the most recent of them; the others are arXiv:1712.06143, arXiv:1310.5504.
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