@phdthesis{Henderson1971,
  author = {Henderson, John Robert},
  title = {Permutation Decompositions of {(0,1)}-Matrices and Decomposition Transversals},
  school = {California Institute of Technology},
  year = {1971},
  doi = {10.7907/J1Z1-SK19},
  note = {\href{https://doi.org/10.7907/J1Z1-SK19}{doi:10.7907/J1Z1-SK19}},
  url = {https://thesis.caltech.edu/5726/}
}

@article{Aharoni2001,
  author = {Aharoni, Ron},
  title = {{Ryser}'s conjecture for tripartite 3-graphs},
  journal = {Combinatorica},
  volume = {21},
  number = {1},
  pages = {1--4},
  year = {2001},
  doi = {10.1007/s004930170001},
  note = {\href{https://doi.org/10.1007/s004930170001}{doi:10.1007/s004930170001}},
  url = {https://doi.org/10.1007/s004930170001}
}

@article{Tuza1983,
  author = {Tuza, Zsolt},
  title = {{Ryser}'s conjecture on transversals of {$r$}-partite hypergraphs},
  journal = {Ars Combinatoria},
  volume = {16B},
  pages = {201--209},
  year = {1983},
  note = {\href{https://combinatorialpress.com/ars/vol16b/}{Publisher record}},
  url = {https://combinatorialpress.com/ars/vol16b/}
}

@article{BDMS2021,
  author = {Bishnoi, Anurag and Das, Shagnik and Morris, Patrick and Szab{\'o}, Tibor},
  title = {{Ryser}'s conjecture for {$t$}-intersecting hypergraphs},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {179},
  pages = {105366},
  year = {2021},
  doi = {10.1016/j.jcta.2020.105366},
  note = {\href{https://doi.org/10.1016/j.jcta.2020.105366}{doi:10.1016/j.jcta.2020.105366}},
  eprint = {2001.04132},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  url = {https://arxiv.org/abs/2001.04132}
}

@article{BKT2004,
  author = {Bourgain, Jean and Katz, Nets and Tao, Terence},
  title = {A sum-product estimate in finite fields, and applications},
  journal = {Geometric and Functional Analysis},
  volume = {14},
  number = {1},
  pages = {27--57},
  year = {2004},
  doi = {10.1007/s00039-004-0451-1},
  note = {\href{https://doi.org/10.1007/s00039-004-0451-1}{doi:10.1007/s00039-004-0451-1}},
  eprint = {math/0301343},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  url = {https://arxiv.org/abs/math/0301343}
}

@article{Petridis2012,
  author = {Petridis, Giorgis},
  title = {New proofs of {Pl{\"u}nnecke}-type estimates for product sets in groups},
  journal = {Combinatorica},
  volume = {32},
  number = {6},
  pages = {721--733},
  year = {2012},
  doi = {10.1007/s00493-012-2818-5},
  note = {\href{https://doi.org/10.1007/s00493-012-2818-5}{doi:10.1007/s00493-012-2818-5}},
  eprint = {1101.3507},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  url = {https://arxiv.org/abs/1101.3507}
}

@article{Haxell1995,
  author = {Haxell, P. E.},
  title = {A condition for matchability in hypergraphs},
  journal = {Graphs and Combinatorics},
  volume = {11},
  number = {3},
  pages = {245--248},
  year = {1995},
  doi = {10.1007/BF01793010},
  note = {\href{https://doi.org/10.1007/BF01793010}{doi:10.1007/BF01793010}},
  url = {https://doi.org/10.1007/BF01793010}
}

@article{CHM2025,
  author = {Clow, Alexander and Haxell, Penny and Mohar, Bojan},
  title = {A Counterexample to a Conjecture of {Lov{\'a}sz}},
  journal = {Combinatorica},
  volume = {46},
  pages = {26},
  year = {2026},
  doi = {10.1007/s00493-026-00220-3},
  note = {Article 26. \href{https://doi.org/10.1007/s00493-026-00220-3}{doi:10.1007/s00493-026-00220-3}},
  eprint = {2505.05339},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  url = {https://link.springer.com/article/10.1007/s00493-026-00220-3}
}


@misc{BestWanless2018,
  author = {Best, Darcy and Wanless, Ian M.},
  title = {What did {Ryser} Conjecture?},
  year = {2018},
  eprint = {1801.02893},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  url = {https://arxiv.org/abs/1801.02893},
  note = {\href{https://arxiv.org/abs/1801.02893}{arXiv:1801.02893}}
}

@article{HaxellScott2012,
  author = {Haxell, P. E. and Scott, A. D.},
  title = {On {Ryser}'s conjecture},
  journal = {The Electronic Journal of Combinatorics},
  volume = {19},
  number = {1},
  pages = {P23},
  year = {2012},
  doi = {10.37236/1175},
  note = {\href{https://doi.org/10.37236/1175}{doi:10.37236/1175}}
}

@article{MansourSongYuster2009,
  author = {Mansour, Toufik and Song, Chunwei and Yuster, Raphael},
  title = {A comment on {Ryser}'s conjecture for intersecting hypergraphs},
  journal = {Graphs and Combinatorics},
  volume = {25},
  number = {1},
  pages = {101--109},
  year = {2009},
  doi = {10.1007/s00373-008-0821-9},
  eprint = {0709.3138},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0709.3138},
  note = {\href{https://arxiv.org/abs/0709.3138}{arXiv:0709.3138}}
}

@article{AharoniBaratWanless2016,
  author = {Aharoni, Ron and Bar{\'a}t, J{\'a}nos and Wanless, Ian M.},
  title = {Multipartite hypergraphs achieving equality in {Ryser}'s conjecture},
  journal = {Graphs and Combinatorics},
  volume = {32},
  number = {1},
  pages = {1--15},
  year = {2016},
  doi = {10.1007/s00373-015-1575-9},
  eprint = {1409.4833},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1409.4833},
  note = {\href{https://arxiv.org/abs/1409.4833}{arXiv:1409.4833}}
}

@article{FranceticHerkeMcKayWanless2017,
  author = {Franceti{\'c}, Nevena and Herke, Sarada and McKay, Brendan D. and Wanless, Ian M.},
  title = {On {Ryser}'s conjecture for linear intersecting multipartite hypergraphs},
  journal = {European Journal of Combinatorics},
  volume = {61},
  pages = {91--105},
  year = {2017},
  doi = {10.1016/j.ejc.2016.10.004},
  eprint = {1508.00951},
  archivePrefix = {arXiv},
  note = {\href{https://doi.org/10.1016/j.ejc.2016.10.004}{doi:10.1016/j.ejc.2016.10.004}}
}

@article{AbuKhaznehBaratPokrovskiySzabo2019,
  author = {Abu-Khazneh, Ahmad and Bar{\'a}t, J{\'a}nos and Pokrovskiy, Alexey and Szab{\'o}, Tibor},
  title = {A family of extremal hypergraphs for {Ryser}'s conjecture},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {161},
  pages = {164--177},
  year = {2019},
  doi = {10.1016/j.jcta.2018.07.011},
  eprint = {1605.06361},
  archivePrefix = {arXiv},
  note = {\href{https://doi.org/10.1016/j.jcta.2018.07.011}{doi:10.1016/j.jcta.2018.07.011}}
}

@article{HaxellScott2017,
  author = {Haxell, P. E. and Scott, A. D.},
  title = {A note on intersecting hypergraphs with large cover number},
  journal = {The Electronic Journal of Combinatorics},
  volume = {24},
  number = {3},
  pages = {P3.26},
  year = {2017},
  doi = {10.37236/6460},
  eprint = {1609.05458},
  archivePrefix = {arXiv},
  note = {\href{https://doi.org/10.37236/6460}{doi:10.37236/6460}}
}

@incollection{Ruzsa1999,
  author = {Ruzsa, Imre Z.},
  title = {An analog of {Freiman}'s theorem in groups},
  booktitle = {Structure theory of set addition},
  series = {Ast{\'e}risque},
  publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France},
  volume = {258},
  pages = {323--326},
  year = {1999},
  url = {https://www.numdam.org/item/AST_1999__258__323_0/},
  note = {\href{https://www.numdam.org/item/AST_1999__258__323_0/}{Primary source}}
}

@article{Gowers1998,
  author = {Gowers, W. T.},
  title = {A new proof of {Szemer{\'e}di}'s theorem for arithmetic progressions of length four},
  journal = {Geometric and Functional Analysis},
  volume = {8},
  number = {3},
  pages = {529--551},
  year = {1998},
  doi = {10.1007/s000390050065},
  url = {https://doi.org/10.1007/s000390050065},
  note = {\href{https://doi.org/10.1007/s000390050065}{doi:10.1007/s000390050065}}
}

@article{BalogSzemeredi1994,
  author = {Balog, Antal and Szemer{\'e}di, Endre},
  title = {A statistical theorem of set addition},
  journal = {Combinatorica},
  volume = {14},
  number = {3},
  pages = {263--268},
  year = {1994},
  doi = {10.1007/BF01212974},
  url = {https://doi.org/10.1007/BF01212974},
  note = {\href{https://doi.org/10.1007/BF01212974}{doi:10.1007/BF01212974}}
}

@article{FoxSudakov2011,
  author = {Fox, Jacob and Sudakov, Benny},
  title = {Dependent random choice},
  journal = {Random Structures \& Algorithms},
  volume = {38},
  number = {1--2},
  pages = {68--99},
  year = {2011},
  doi = {10.1002/rsa.20344},
  eprint = {0909.3271},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0909.3271},
  note = {\href{https://arxiv.org/abs/0909.3271}{arXiv:0909.3271}}
}

@article{Haxell2001,
  author = {Haxell, P. E.},
  title = {A note on vertex list colouring},
  journal = {Combinatorics, Probability and Computing},
  volume = {10},
  number = {4},
  pages = {345--347},
  year = {2001},
  doi = {10.1017/S0963548301004758},
  url = {https://doi.org/10.1017/S0963548301004758},
  note = {\href{https://doi.org/10.1017/S0963548301004758}{doi:10.1017/S0963548301004758}}
}

@article{Freedman1975,
  author={Freedman, David A.},
  title={On tail probabilities for martingales},
  journal={The Annals of Probability},
  volume={3}, number={1}, pages={100--118}, year={1975},
  doi={10.1214/aop/1176996452},
  note = {\href{https://doi.org/10.1214/aop/1176996452}{doi:10.1214/aop/1176996452}}
}

@article{Jamison1977,
  author={Jamison, Robert E.},
  title={Covering finite fields with cosets of subspaces},
  journal={Journal of Combinatorial Theory, Series A},
  volume={22}, number={3}, pages={253--266}, year={1977},
  doi={10.1016/0097-3165(77)90001-2},
  note = {\href{https://doi.org/10.1016/0097-3165(77)90001-2}{doi:10.1016/0097-3165(77)90001-2}}
}

@article{BrouwerSchrijver1978,
  author={Brouwer, A. E. and Schrijver, A.},
  title={The blocking number of an affine space},
  journal={Journal of Combinatorial Theory, Series A},
  volume={24}, number={2}, pages={251--253}, year={1978},
  doi={10.1016/0097-3165(78)90013-4},
  note = {\href{https://doi.org/10.1016/0097-3165(78)90013-4}{doi:10.1016/0097-3165(78)90013-4}}
}

@article{BBS2010,
  author={Blokhuis, A. and Brouwer, A. E. and Sz{\H o}nyi, T.},
  title={Covering all points except one},
  journal={Journal of Algebraic Combinatorics},
  volume={32}, pages={59--66}, year={2010},
  doi={10.1007/s10801-009-0204-1},
  note = {\href{https://doi.org/10.1007/s10801-009-0204-1}{doi:10.1007/s10801-009-0204-1}}
}

@misc{White2026,
  author = {White, Patrick},
  title = {{Tuza}'s {Ryser}-conjecture claim for four-partite hypergraphs with matching number two},
  year = {2026},
  eprint = {2609.14281},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  note = {Version 1, 13 September 2026},
  howpublished = {\href{https://arxiv.org/abs/2609.14281v1}{arXiv:2609.14281v1}},
  url = {https://arxiv.org/abs/2609.14281v1}
}


@misc{OpenAI2026Balanced,
  author = {{OpenAI}},
  title = {{Balanced counterexamples to Ryser's conjecture at prime orders}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Balanced-Counterexamples-to-Rysers-Conjecture-at-Prime-Orders-September-27-2026/paper.pdf}{OAI:Balanced-Counterexamples-to-Rysers-Conjecture-at-Prime-Orders-September-27-2026}},
  year = {2026}
}

@misc{AbiadGarbePovillSpiegel2025,
  author = {Abiad, Aida and Garbe, Frederik and Povill, Xavier and Spiegel, Christoph},
  title = {Infinitely many counterexamples to a conjecture of {Lov{\'a}sz}},
  year = {2025},
  eprint = {2506.21286},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  note = {Version 2, 14 July 2025},
  howpublished = {\href{https://arxiv.org/abs/2506.21286v2}{arXiv:2506.21286v2}},
  url = {https://arxiv.org/abs/2506.21286v2}
}

@article{KiralyTothmeresz2017,
  author = {Kir{\'a}ly, Zolt{\'a}n and T{\'o}thm{\'e}r{\'e}sz, Lilla},
  title = {On {Ryser}'s Conjecture for $t$-Intersecting and Degree-Bounded Hypergraphs},
  journal = {The Electronic Journal of Combinatorics},
  volume = {24},
  number = {4},
  pages = {P4.40},
  year = {2017},
  doi = {10.37236/6448},
  eprint = {1705.10024},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  note = {\href{https://doi.org/10.37236/6448}{doi:10.37236/6448}}
}

@article{ErdosGyarfasPyber1991,
  author = {Erd{\H{o}}s, P. and Gy{\'a}rf{\'a}s, A. and Pyber, L.},
  title = {Vertex coverings by monochromatic cycles and trees},
  journal = {Journal of Combinatorial Theory, Series B},
  volume = {51},
  number = {1},
  pages = {90--95},
  year = {1991},
  doi = {10.1016/0095-8956(91)90007-7},
  note = {\href{https://doi.org/10.1016/0095-8956(91)90007-7}{doi:10.1016/0095-8956(91)90007-7}},
  url = {https://doi.org/10.1016/0095-8956(91)90007-7}
}

@misc{Milicevic2017,
  author = {Mili{\'c}evi{\'c}, Luka},
  title = {Covering complete graphs by monochromatically bounded sets},
  year = {2017},
  eprint = {1705.09370},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  note = {Version 1, 25 May 2017},
  howpublished = {\href{https://arxiv.org/abs/1705.09370v1}{arXiv:\allowbreak1705.09370v1}},
  url = {https://arxiv.org/abs/1705.09370v1}
}

@misc{DeBiasioKamelMcCourtSheats2021,
  author = {DeBiasio, Louis and Kamel, Yigal and McCourt, Grace and Sheats, Hannah},
  title = {Generalizations and strengthenings of {Ryser}'s conjecture},
  year = {2021},
  eprint = {2009.07239},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  note = {Version 3, 3 November 2021},
  howpublished = {\href{https://arxiv.org/abs/2009.07239v3}{arXiv:2009.07239v3}},
  url = {https://arxiv.org/abs/2009.07239v3}
}
