@article{hadwiger1943,
  author = {Hadwiger, Hugo},
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}

@incollection{duchet1982,
  author = {Duchet, Pierre and Meyniel, Henri},
  title = {On {Hadwiger}'s number and the stability number},
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  address = {Amsterdam},
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}

@article{pst2003,
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}

@article{fox2010,
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@article{fgs2005,
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}

@misc{cambie2021,
  author = {Cambie, Stijn},
  title = {{Hadwiger}'s conjecture implies a conjecture of {F{\"u}redi--Gy{\'a}rf{\'a}s--Simonyi}},
  year = {2021},
  eprint = {2108.10303},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  doi = {10.48550/arXiv.2108.10303},
  note = {arXiv:2108.10303, version 1},
  url = {https://arxiv.org/abs/2108.10303v1}
}

@misc{yip2025,
  author = {Yip, Jung Hon},
  title = {Dense matchings of linear size in graphs with independence number 2},
  year = {2025},
  eprint = {2512.01401},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  doi = {10.48550/arXiv.2512.01401},
  note = {arXiv:2512.01401, version 2},
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}

@book{cover2006,
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}

@article{frieze1999,
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}


@article{csiszar1975,
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@article{laurentmourrain2009,
  author = {Laurent, Monique and Mourrain, Bernard},
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@article{kleitmanwinston1982,
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@article{samotij2015,
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@article{fordfulkerson1956,
  author = {Ford, Jr., L. R. and Fulkerson, D. R.},
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}

@article{Blasiak2007,
  author = {Blasiak, Jonah}, title = {A special case of {Hadwiger}'s conjecture},
  journal = {Journal of Combinatorial Theory, Series B},
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  doi = {10.1016/j.jctb.2007.04.003}
}
@article{ChenDeng2025,
  author = {Chen, Rong and Deng, Zijian},
  title = {Connected Matchings in Graphs with Independence Number Two},
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  pages = {107}, year = {2025}, doi = {10.1007/s00373-025-02971-0},
  eprint = {2409.05920}, archivePrefix = {arXiv}, primaryClass = {math.CO},
  note = {Article 107; preprint version 1 is titled ``Connected matching in graphs with independence number two''}
}
@article{ChudnovskySeymour2012,
  author = {Chudnovsky, Maria and Seymour, Paul}, title = {Packing seagulls},
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@article{NorinSeymour2026,
  author = {Norin, Sergey and Seymour, Paul},
  title = {Dense minors of graphs with independence number two},
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  doi = {10.1016/j.jctb.2025.08.005}, eprint = {2206.00186}, archivePrefix = {arXiv}, primaryClass = {math.CO}
}
@misc{KuhnSauermannSteinerWigderson2025,
  author = {K{\"u}hn, Marcus and Sauermann, Lisa and Steiner, Raphael and Wigderson, Yuval},
  title = {Disproof of the Odd {Hadwiger} Conjecture},
  year = {2025}, eprint = {2512.20392}, archivePrefix = {arXiv}, primaryClass = {math.CO},
  doi = {10.48550/arXiv.2512.20392},
  note = {arXiv:2512.20392, version 1, December 23, 2025},
  url = {https://arxiv.org/abs/2512.20392v1}
}

@article{Wagner1937,
 author={Wagner, Klaus}, title={{\"U}ber eine Eigenschaft der ebenen Komplexe},
 journal={Mathematische Annalen}, volume={114}, pages={570--590}, year={1937},
 doi={10.1007/BF01594196}
}
@article{Dirac1952,
  author = {Dirac, G. A.},
  title = {A property of 4-chromatic graphs and some remarks on critical graphs},
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}
@article{Kostochka1984,
  author = {Kostochka, A. V.},
  title = {Lower bound of the {Hadwiger} number of graphs by their average degree},
  journal = {Combinatorica}, volume = {4}, number = {4},
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  url = {https://kostochk.web.illinois.edu/docs/old/cca84.pdf}
}
@article{Thomason1984,
  author = {Thomason, Andrew},
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@article{NorinPostleSong2023,
  author = {Norin, Sergey and Postle, Luke and Song, Zi-Xia},
  title = {Breaking the degeneracy barrier for coloring graphs with no {$K_t$} minor},
  journal = {Advances in Mathematics}, volume = {422},
  pages = {109020}, year = {2023}, doi = {10.1016/j.aim.2023.109020},
  eprint = {1910.09378}, archivePrefix = {arXiv}, primaryClass = {math.CO}
}
@article{DelcourtPostle2025,
  author = {Delcourt, Michelle and Postle, Luke},
  title = {Reducing Linear {Hadwiger}'s Conjecture to Coloring Small Graphs},
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  eprint = {2108.01633}, archivePrefix = {arXiv}, primaryClass = {math.CO}
}
@misc{LiuLuo2026,
  author = {Liu, Chun-Hung and Luo, Jason},
  title = {Beyond halfway to {Hadwiger}'s conjecture},
  year = {2026}, eprint = {2609.06867}, archivePrefix = {arXiv},
  primaryClass = {math.CO}, doi = {10.48550/arXiv.2609.06867},
  note = {arXiv:2609.06867, version 2, September 9, 2026},
  url = {https://arxiv.org/abs/2609.06867v2}
}
@article{RobertsonSeymourThomas1993,
 author={Robertson, Neil and Seymour, Paul and Thomas, Robin},
 title={{Hadwiger}'s conjecture for {$K_6$}-free graphs},
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 doi={10.1007/BF01202354}, url={https://people.math.gatech.edu/~thomas/PAP/hadwiger.pdf}
}
@article{AppelHaken1977,
 author={Appel, K. and Haken, W.},
 title={Every planar map is four colorable. {Part I}: Discharging},
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 pages={429--490}, year={1977}, doi={10.1215/ijm/1256049011}
}
@article{AppelHakenKoch1977,
 author={Appel, K. and Haken, W. and Koch, J.},
 title={Every planar map is four colorable. {Part II}: Reducibility},
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}

@article{reedseymour1998,
  author = {Reed, Bruce and Seymour, Paul},
  title = {Fractional Colouring and {Hadwiger}'s Conjecture},
  journal = {Journal of Combinatorial Theory, Series B},
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  number = {2},
  pages = {147--152},
  year = {1998},
  doi = {10.1006/jctb.1998.1835},
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}

@misc{OpenAIColinDeVerdiereCounterexample2026,
  author = {{OpenAI}},
  title = {{A counterexample to the Colin de Verdi{\`e}re chromatic conjecture}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture-September-23-2026/paper.pdf}{OAI:A-counterexample-to-the-Colin-de-Verdiere-chromatic-conjecture-September-23-2026}},
  year = {2026}
}