@article{cdv1990,
  author = {Colin de Verdi{\`e}re, Yves},
  title = {Sur un nouvel invariant des graphes et un crit{\`e}re de planarit{\'e}},
  journal = {Journal of Combinatorial Theory, Series B},
  volume = {50},
  number = {1},
  pages = {11--21},
  year = {1990},
  doi = {10.1016/0095-8956(90)90093-F},
  url = {https://doi.org/10.1016/0095-8956(90)90093-F}
}

@book{cdv1998,
  author = {Colin de Verdi{\`e}re, Yves},
  title = {Spectres de graphes},
  series = {Cours Sp{\'e}cialis{\'e}s},
  volume = {4},
  publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France},
  address = {Paris},
  year = {1998},
  isbn = {2-85629-068-X},
  url = {https://smf.emath.fr/node/43207}
}

@incollection{hls1999,
  author = {van der Holst, Hein and Lov{\'a}sz, L{\'a}szl{\'o} and Schrijver, Alexander},
  title = {The {Colin de Verdi{\`e}re} graph parameter},
  booktitle = {Graph Theory and Combinatorial Biology},
  series = {Bolyai Society Mathematical Studies},
  volume = {7},
  pages = {29--85},
  publisher = {J{\'a}nos Bolyai Mathematical Society},
  address = {Budapest},
  year = {1999},
  url = {https://ir.cwi.nl/pub/1257/1257D.pdf}
}

@incollection{lovaszschrijver2017,
  author = {Lov{\'a}sz, L{\'a}szl{\'o} and Schrijver, Alexander},
  title = {Nullspace embeddings for outerplanar graphs},
  booktitle = {A Journey Through Discrete Mathematics},
  editor = {Loebl, Martin and Ne{\v{s}}et{\v{r}}il, Jaroslav and Thomas, Robin},
  pages = {571--591},
  publisher = {Springer},
  address = {Cham},
  year = {2017},
  doi = {10.1007/978-3-319-44479-6_23},
  url = {https://ir.cwi.nl/pub/27485/27485.pdf}
}

@article{hadwiger1943,
  author = {Hadwiger, Hugo},
  title = {{\"U}ber eine {Klassifikation} der {Streckenkomplexe}},
  journal = {Vierteljahrsschrift der Naturforschenden Gesellschaft in Z{\"u}rich},
  volume = {88},
  pages = {133--142},
  year = {1943},
  url = {https://ngzh.ch/wp-content/uploads/2024/08/88_17.pdf}
}

@incollection{duchet1982,
  author = {Duchet, Pierre and Meyniel, Henri},
  title = {On {Hadwiger}'s number and the stability number},
  booktitle = {Graph Theory (Cambridge, 1981)},
  series = {North-Holland Mathematics Studies},
  volume = {62},
  pages = {71--73},
  publisher = {North-Holland},
  address = {Amsterdam},
  year = {1982}
}

@article{pst2003,
  author = {Plummer, Michael D. and Stiebitz, Michael and Toft, Bjarne},
  title = {On a special case of {Hadwiger}'s conjecture},
  journal = {Discussiones Mathematicae Graph Theory},
  volume = {23},
  number = {2},
  pages = {333--363},
  year = {2003},
  doi = {10.7151/dmgt.1206},
  url = {https://d-nb.info/120400434X/34}
}

@article{fox2010,
  author = {Fox, Jacob},
  title = {Complete minors and independence number},
  journal = {SIAM Journal on Discrete Mathematics},
  volume = {24},
  number = {4},
  pages = {1313--1321},
  year = {2010},
  doi = {10.1137/090766814},
  url = {https://epubs.siam.org/doi/10.1137/090766814}
}

@article{fgs2005,
  author = {F{\"u}redi, Zolt{\'a}n and Gy{\'a}rf{\'a}s, Andr{\'a}s and Simonyi, G{\'a}bor},
  title = {Connected matchings and {Hadwiger}'s conjecture},
  journal = {Combinatorics, Probability and Computing},
  volume = {14},
  number = {3},
  pages = {435--438},
  year = {2005},
  doi = {10.1017/S0963548305006759},
  url = {https://doi.org/10.1017/S0963548305006759}
}

@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},
  url = {https://arxiv.org/abs/2512.01401v2}
}

@book{cover2006,
  author = {Cover, Thomas M. and Thomas, Joy A.},
  title = {Elements of Information Theory},
  edition = {Second},
  publisher = {John Wiley \& Sons},
  year = {2006},
  isbn = {978-0-471-24195-9},
  doi = {10.1002/047174882X},
  url = {https://onlinelibrary.wiley.com/doi/book/10.1002/047174882X}
}

@article{frieze1999,
  author = {Frieze, Alan and Kannan, Ravi},
  title = {Quick approximation to matrices and applications},
  journal = {Combinatorica},
  volume = {19},
  pages = {175--220},
  year = {1999},
  doi = {10.1007/s004930050052},
  url = {https://link.springer.com/article/10.1007/s004930050052}
}

@article{csiszar1975,
  author = {Csisz{\'a}r, Imre},
  title = {{$I$}-Divergence Geometry of Probability Distributions and Minimization Problems},
  journal = {The Annals of Probability},
  volume = {3}, number = {1}, pages = {146--158}, year = {1975},
  doi = {10.1214/aop/1176996454}
}


@article{laurentmourrain2009,
  author = {Laurent, Monique and Mourrain, Bernard},
  title = {A generalized flat extension theorem for moment matrices},
  journal = {Archiv der Mathematik}, volume = {93}, number = {1},
  pages = {87--98}, year = {2009}, doi = {10.1007/s00013-009-0007-6},
  eprint = {0812.2563}, archivePrefix = {arXiv}
}


@article{kleitmanwinston1982,
  author = {Kleitman, Daniel J. and Winston, Kenneth J.},
  title = {On the number of graphs without 4-cycles},
  journal = {Discrete Mathematics}, volume = {41}, number = {2},
  pages = {167--172}, year = {1982}, doi = {10.1016/0012-365X(82)90204-7}
}


@article{samotij2015,
  author = {Samotij, Wojciech},
  title = {Counting independent sets in graphs},
  journal = {European Journal of Combinatorics}, volume = {48},
  pages = {5--18}, year = {2015}, doi = {10.1016/j.ejc.2015.02.005},
  eprint = {1412.0940}, archivePrefix = {arXiv}
}


@article{fordfulkerson1956,
  author = {Ford, Jr., L. R. and Fulkerson, D. 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{menger1927,
  author = {Menger, Karl}, title = {Zur allgemeinen Kurventheorie},
  journal = {Fundamenta Mathematicae}, volume = {10},
  pages = {96--115}, year = {1927}, doi = {10.4064/fm-10-1-96-115}
}


@incollection{galekuhntucker1951,
  author = {Gale, David and Kuhn, Harold W. and Tucker, Albert W.},
  title = {Linear Programming and the Theory of Games},
  booktitle = {Activity Analysis of Production and Allocation},
  editor = {Koopmans, Tjalling C.},
  series = {Cowles Commission Monographs}, volume = {13},
  chapter = {19}, pages = {317--329},
  publisher = {John Wiley \& Sons}, year = {1951}
}


@article{azuma1967,
  author = {Azuma, Kazuoki},
  title = {Weighted sums of certain dependent random variables},
  journal = {Tohoku Mathematical Journal, Second Series},
  volume = {19}, number = {3}, pages = {357--367}, year = {1967},
  doi = {10.2748/tmj/1178243286}
}


@incollection{mcdiarmid1989,
  author = {McDiarmid, Colin}, title = {On the method of bounded differences},
  booktitle = {Surveys in Combinatorics, 1989}, editor = {Siemons, J.},
  series = {London Mathematical Society Lecture Note Series}, volume = {141},
  pages = {148--188}, publisher = {Cambridge University Press}, year = {1989},
  doi = {10.1017/CBO9781107359949.008}
}

@article{cdv1988arnold,
  author = {Colin de Verdi{\`e}re, Yves},
  title = {Sur une hypoth{\`e}se de transversalit{\'e} d'{Arnold}},
  journal = {Commentarii Mathematici Helvetici},
  volume = {63}, pages = {184--193}, year = {1988},
  url = {https://www-fourier.univ-grenoble-alpes.fr/~ycolver/All-Articles/88a.pdf}
}


@incollection{cdv1999operators,
  author = {Colin de Verdi{\`e}re, Yves},
  title = {Spectres d'op{\'e}rateurs diff{\'e}rentiels sur les graphes},
  booktitle = {Random Walks and Discrete Potential Theory},
  series = {Symposia Mathematica}, volume = {39},
  publisher = {Cambridge University Press}, pages = {139--165}, year = {1999},
  url = {https://www-fourier.univ-grenoble-alpes.fr/~ycolver/All-Articles/99d.pdf}
}


@article{lovaszschrijver1998,
  author = {Lov{\'a}sz, L{\'a}szl{\'o} and Schrijver, Alexander},
  title = {A {Borsuk} theorem for antipodal links and a spectral characterization of linklessly embeddable graphs},
  journal = {Proceedings of the American Mathematical Society},
  volume = {126}, number = {5}, pages = {1275--1285}, year = {1998},
  url = {https://homepages.cwi.nl/~lex/files/link.pdf}
}


@article{lovaszschrijver1999,
  author = {Lov{\'a}sz, L{\'a}szl{\'o} and Schrijver, Alexander},
  title = {On the null space of a {Colin de Verdi{\`e}re} matrix},
  journal = {Annales de l'Institut Fourier},
  volume = {49}, number = {3}, pages = {1017--1026}, year = {1999},
  doi = {10.5802/aif.1703},
  url = {https://www.numdam.org/item/10.5802/aif.1703.pdf}
}


@article{kotlovlovaszvempala1997,
  author = {Kotlov, Andrew and Lov{\'a}sz, L{\'a}szl{\'o} and Vempala, Santosh},
  title = {The {Colin de Verdi{\`e}re} number and sphere representations of a graph},
  journal = {Combinatorica}, volume = {17}, number = {4},
  pages = {483--521}, year = {1997}, doi = {10.1007/BF01195002}
}


@article{schrijversevenster2017,
  author = {Schrijver, Alexander and Sevenster, Bart},
  title = {The {Strong Arnold Property} for 4-connected flat graphs},
  journal = {Linear Algebra and its Applications}, volume = {522},
  pages = {153--160}, year = {2017}, doi = {10.1016/j.laa.2017.02.002},
  url = {https://ir.cwi.nl/pub/26811/26811.pdf}
}


@misc{kaluzakoval2024,
  author = {Kalu{\v{z}}a, Vojt{\v{e}}ch and Koval, Vadym},
  title = {Three observations on the {Colin de Verdi{\`e}re} spectral graph parameter},
  year = {2024}, eprint = {2410.21226}, archivePrefix = {arXiv},
  primaryClass = {math.CO}, doi = {10.48550/arXiv.2410.21226},
  url = {https://arxiv.org/abs/2410.21226}
}

@incollection{Gromov1987Hyperbolic,
  author = {Gromov, M.},
  title = {Hyperbolic groups},
  editor = {Gersten, S. M.},
  booktitle = {Essays in Group Theory},
  series = {Mathematical Sciences Research Institute Publications},
  volume = {8},
  pages = {75--263},
  publisher = {Springer},
  address = {New York},
  year = {1987},
  doi = {10.1007/978-1-4613-9586-7_3}
}


@article{CornectMartinezPedroza2025Tree,
  author = {Cornect, Anders and Mart{\'i}nez-Pedroza, Eduardo},
  title = {{Gromov}'s approximating tree and the all-pairs bottleneck paths problem},
  journal = {Involve},
  note = {To appear; arXiv:2408.05338v2},
  year = {2025},
  eprint = {2408.05338},
  archivePrefix = {arXiv},
  primaryClass = {cs.CG},
  url = {https://arxiv.org/abs/2408.05338v2}
}


@article{FiedlerSchneider1983Analytic,
  author = {Fiedler, Miroslav and Schneider, Hans},
  title = {Analytic functions of {$M$}-matrices and generalizations},
  journal = {Linear and Multilinear Algebra},
  volume = {13},
  number = {3},
  pages = {185--201},
  year = {1983},
  doi = {10.1080/03081088308817519}
}


@article{DebreuHerstein1953Nonnegative,
  author = {Debreu, Gerard and Herstein, I. N.},
  title = {Nonnegative square matrices},
  journal = {Econometrica},
  volume = {21},
  number = {4},
  pages = {597--607},
  year = {1953},
  doi = {10.2307/1907925}
}


@article{ChenHeZhang2025Stiefel,
  author = {Chen, Xiaojun and He, Yifan and Zhang, Zaikun},
  title = {Tight error bounds for the sign-constrained {Stiefel} manifold},
  journal = {SIAM Journal on Optimization},
  volume = {35},
  number = {1},
  pages = {302--329},
  year = {2025},
  doi = {10.1137/24M1659030}
}


@article{JiangMengWenChen2023Nonnegative,
  author = {Jiang, Bo and Meng, Xiao and Wen, Zaiwen and Chen, Xiaojun},
  title = {An exact penalty approach for optimization with nonnegative orthogonality constraints},
  journal = {Mathematical Programming},
  volume = {198},
  pages = {855--897},
  year = {2023},
  doi = {10.1007/s10107-022-01794-8}
}

@article{reedseymour1998,
  author = {Reed, Bruce and Seymour, Paul},
  title = {Fractional Colouring and {Hadwiger}'s Conjecture},
  journal = {Journal of Combinatorial Theory, Series B},
  volume = {74},
  number = {2},
  pages = {147--152},
  year = {1998},
  doi = {10.1006/jctb.1998.1835},
  url = {https://cgm.cs.mcgill.ca/~breed/SummerNSERC04/frachad.pdf}
}

@misc{OpenAILinearListHadwiger2026,
  author = {{OpenAI}},
  title = {{A linear list-coloring bound in terms of the Hadwiger number}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-linear-list-coloring-bound-in-terms-of-the-Hadwiger-number-September-23-2026/paper.pdf}{OAI:A-linear-list-coloring-bound-in-terms-of-the-Hadwiger-number-September-23-2026}},
  year = {2026}
}

@misc{OpenAIHadwigerCounterexample2026,
  author = {{OpenAI}},
  title = {{A counterexample to Hadwiger's conjecture}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-counterexample-to-Hadwigers-conjecture-September-23-2026/paper.pdf}{OAI:A-counterexample-to-Hadwigers-conjecture-September-23-2026}},
  year = {2026}
}
