@incollection{Barnette1969,
  author    = {Gr{\"u}nbaum, Branko},
  title     = {Unsolved Problem 5},
  booktitle = {Recent Progress in Combinatorics: Proceedings of the Third
               Waterloo Conference on Combinatorics, May 1968},
  editor    = {Tutte, William T.},
  publisher = {Academic Press},
  address   = {New York},
  year      = {1969},
  pages     = {343},
  note      = {Conjecture attributed to David W. Barnette}
}

@article{APSW2016,
  author        = {Alt, Helmut and Payne, Michael S. and Schmidt, Jens M.
                   and Wood, David R.},
  title         = {Thoughts on {Barnette}'s Conjecture},
  journal       = {Australasian Journal of Combinatorics},
  volume        = {64},
  number        = {2},
  year          = {2016},
  pages         = {354--365},
  url           = {https://arxiv.org/abs/1312.3783v1},
  eprint        = {1312.3783},
  archivePrefix = {arXiv},
  primaryClass  = {math.CO}
}

@misc{HK2018,
  author        = {Hine, Camden and K{\'a}lm{\'a}n, Tam{\'a}s},
  title         = {Clock theorems for triangulated surfaces},
  year          = {2018},
  howpublished  = {arXiv:1808.06091v1},
  doi           = {10.48550/arXiv.1808.06091},
  url           = {https://arxiv.org/abs/1808.06091v1},
  eprint        = {1808.06091},
  archivePrefix = {arXiv},
  primaryClass  = {math.CO}
}

@article{GSW2023,
  author        = {Gorsky, Maximilian and Steiner, Raphael and Wiederrecht,
                   Sebastian},
  title         = {Matching theory and {Barnette}'s conjecture},
  journal       = {Discrete Mathematics},
  volume        = {346},
  number        = {2},
  year          = {2023},
  pages         = {113249},
  doi           = {10.1016/j.disc.2022.113249},
  url           = {https://arxiv.org/abs/2202.11641v3},
  eprint        = {2202.11641},
  archivePrefix = {arXiv},
  primaryClass  = {math.CO},
  note          = {Theorem numbering follows arXiv:2202.11641v3,
                   15 August 2022}
}

@article{Tutte1946,
  author = {Tutte, William T.},
  title = {On {Hamiltonian} Circuits},
  journal = {Journal of the London Mathematical Society},
  volume = {s1-21}, number = {2}, pages = {98--101}, year = {1946},
  doi = {10.1112/jlms/s1-21.2.98}
}
@article{Stein1971,
  author = {Stein, Sherman K.},
  title = {{$B$}-sets and planar maps},
  journal = {Pacific Journal of Mathematics},
  volume = {37}, number = {1}, pages = {217--224}, year = {1971},
  url = {https://msp.org/pjm/1971/37-1/pjm-v37-n1-p20-s.pdf}
}
@article{Goodey1975,
  author = {Goodey, Paul R.},
  title = {Hamiltonian circuits in polytopes with even sided faces},
  journal = {Israel Journal of Mathematics},
  volume = {22}, pages = {52--56}, year = {1975},
  doi = {10.1007/BF02757273}
}
@techreport{FederSubi2006,
  author = {Feder, Tom{\'a}s and Subi, Carlos},
  title = {On {Barnette}'s conjecture},
  institution = {Electronic Colloquium on Computational Complexity},
  number = {TR06-015}, year = {2006},
  url = {https://eccc.weizmann.ac.il/report/2006/015/}
}
@article{Kardos2020,
  author = {Kardo{\v{s}}, Franti{\v{s}}ek},
  title = {A Computer-Assisted Proof of the {Barnette--Goodey} Conjecture:
           Not Only Fullerene Graphs Are {Hamiltonian}},
  journal = {SIAM Journal on Discrete Mathematics},
  volume = {34}, number = {1}, pages = {62--100}, year = {2020},
  doi = {10.1137/140984737},
  eprint = {1409.2440}, archivePrefix = {arXiv}, primaryClass = {math.CO},
  url = {https://arxiv.org/abs/1409.2440v2}
}
@techreport{Hertel2005,
  author = {Hertel, Alexander},
  title = {A Survey and Strengthening of {Barnette}'s Conjecture},
  institution = {Department of Computer Science, University of Toronto},
  year = {2005},
  url = {https://www.cs.toronto.edu/~ahertel/WebPageFiles/Papers/StrengtheningBarnette'sConjecture10.pdf}
}
@incollection{Tutte1975,
  author = {Tutte, William T.},
  title = {Duality and trinity},
  booktitle = {Infinite and Finite Sets},
  editor = {Hajnal, Andr{\'a}s and Rado, Richard and S{\'o}s, Vera T.},
  series = {Colloquia Mathematica Societatis J{\'a}nos Bolyai},
  volume = {10}, pages = {1459--1472},
  publisher = {North-Holland}, address = {Amsterdam}, year = {1975},
  note = {Volume III; proceedings of the 1973 Keszthely colloquium}
}
@article{FF1956,
  author = {Ford, Jr., Lester R. and Fulkerson, Delbert R.},
  title = {Maximal Flow Through a Network},
  journal = {Canadian Journal of Mathematics},
  volume = {8}, pages = {399--404}, year = {1956},
  doi = {10.4153/CJM-1956-045-5}
}
@article{KPW2000,
  author = {Kenyon, Richard W. and Propp, James G. and Wilson, David B.},
  title = {Trees and matchings},
  journal = {Electronic Journal of Combinatorics},
  volume = {7}, number = {1}, pages = {R25}, year = {2000},
  doi = {10.37236/1503},
  eprint = {math/9903025}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/9903025v2}
}
@article{Kenyon2014,
  author = {Kenyon, Richard},
  title = {Conformal Invariance of Loops in the Double-Dimer Model},
  journal = {Communications in Mathematical Physics},
  volume = {326}, number = {2}, pages = {477--497}, year = {2014},
  doi = {10.1007/s00220-013-1881-0},
  eprint = {1105.4158}, archivePrefix = {arXiv}, primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1105.4158v2}
}

@misc{Schnieders2025,
  author = {Tobias Schnieders},
  title = {{Barnette} Graphs with Faces up to Size 8 are Hamiltonian},
  year = {2025},
  eprint = {2508.03531},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  doi = {10.48550/arXiv.2508.03531},
  url = {https://arxiv.org/abs/2508.03531v1},
  note = {Version 1, 5 August 2025}
}