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@article{Tabachnikov2008,
  author  = {Tabachnikov, Serge},
  title   = {Converse {S}turm--{H}urwitz--{K}ellogg theorem and related results},
  journal = {J. Fixed Point Theory Appl.},
  volume  = {3},
  number  = {1},
  year    = {2008},
  pages   = {121--130},
  doi     = {10.1007/s11784-007-0049-y},
  note    = {\url{https://doi.org/10.1007/s11784-007-0049-y}; \href{https://arxiv.org/abs/0710.5902}{arXiv:0710.5902}},
}

@article{Tabachnikov2000,
  author  = {Tabachnikov, Serge},
  title   = {A four vertex theorem for polygons},
  journal = {Amer. Math. Monthly},
  volume  = {107},
  number  = {9},
  year    = {2000},
  pages   = {830--833},
  doi     = {10.1080/00029890.2000.12005277},
  note    = {\url{https://doi.org/10.1080/00029890.2000.12005277}},
}

@article{Dahlberg2008,
  author  = {Dahlberg, Bj{\"o}rn E. J.},
  title   = {A discrete four vertex theorem},
  journal = {Geom. Dedicata},
  volume  = {133},
  year    = {2008},
  pages   = {111--128},
  doi     = {10.1007/s10711-008-9238-0},
  note    = {\url{https://doi.org/10.1007/s10711-008-9238-0}},
}

@article{Dahlberg2005,
  author  = {Dahlberg, Bj{\"o}rn E. J.},
  title   = {The converse of the four vertex theorem},
  journal = {Proc. Amer. Math. Soc.},
  volume  = {133},
  number  = {7},
  year    = {2005},
  pages   = {2131--2135},
  doi     = {10.1090/S0002-9939-05-07788-9},
  note    = {\url{https://doi.org/10.1090/S0002-9939-05-07788-9}},
}

@article{Gluck1971,
  author  = {Gluck, Herman},
  title   = {The converse to the four vertex theorem},
  journal = {Enseign. Math. (2)},
  volume  = {17},
  year    = {1971},
  pages   = {295--309},
  doi     = {10.5169/seals-44584},
  note    = {\url{https://doi.org/10.5169/seals-44584}},
}

@article{DGPV2007,
  author  = {DeTurck, Dennis and Gluck, Herman and Pomerleano, Daniel and Vick, David Shea},
  title   = {The four vertex theorem and its converse},
  journal = {Notices Amer. Math. Soc.},
  volume  = {54},
  number  = {2},
  year    = {2007},
  pages   = {192--207},
  note    = {\url{https://arxiv.org/abs/math/0609268}},
}

@article{Musin2004,
  author  = {Musin, Oleg R.},
  title   = {Curvature extrema and four-vertex theorems for polygons and polyhedra},
  journal = {J. Math. Sci. (N.Y.)},
  volume  = {119},
  number  = {2},
  year    = {2004},
  pages   = {268--277},
  doi     = {10.1023/B:JOTH.0000008769.58818.6d},
  note    = {\url{https://doi.org/10.1023/B:JOTH.0000008769.58818.6d}; Revised version: \href{https://arxiv.org/abs/0805.0629v3}{arXiv:0805.0629v3}},
}

@incollection{Sedykh1997,
  author    = {Sedykh, Vyacheslav D.},
  title     = {Discrete versions of the four-vertex theorem},
  booktitle = {Topics in Singularity Theory},
  series    = {Amer. Math. Soc. Transl. Ser. 2},
  volume    = {180},
  publisher = {Amer. Math. Soc.},
  year      = {1997},
  pages     = {197--207},
  doi       = {10.1090/trans2/180/17},
  note    = {\url{https://doi.org/10.1090/trans2/180/17}},
}

@article{Wegner1994,
  author  = {Wegner, Bernd},
  title   = {On the evolutes of piecewise linear curves in the plane},
  journal = {Rad Hrvatske Akad. Znan. Umjet. Mat. Znan.},
  volume  = {11 (467)},
  year    = {1994},
  pages   = {1--16},
  note    = {\url{https://dizbi.hazu.hr/?pr=i&id=172424}},
}

@article{OvsienkoTabachnikov2001,
  author  = {Ovsienko, Valentin and Tabachnikov, Serge},
  title   = {Projective geometry of polygons and discrete 4-vertex and 6-vertex theorems},
  journal = {Enseign. Math. (2)},
  volume  = {47},
  number  = {1--2},
  year    = {2001},
  pages   = {3--19},
  doi     = {10.5169/seals-65426},
  note    = {\url{https://doi.org/10.5169/seals-65426}; \href{https://arxiv.org/abs/math/9909150}{arXiv:math/9909150}},
}

@article{Bilinski1963,
  author  = {Bilinski, Stanko},
  title   = {Die primitivste {F}orm des {V}ierscheitelsatzes},
  journal = {Glasnik Mat.-Fiz. Astronom. Dru\v{s}tvo Mat. Fiz. Hrvatske Ser. II},
  volume  = {18},
  year    = {1963},
  pages   = {85--93},
}

@misc{Pak2010,
  author = {Pak, Igor},
  title  = {Lectures on Discrete and Polyhedral Geometry},
  year   = {2010},
  note    = {Draft, April 20, 2010; \url{https://www.math.ucla.edu/~pak/geompol8.pdf}},
}

@article{GrantMogilski2023,
  author  = {Grant, Kyle and Mogilski, Wiktor},
  title   = {A discrete four vertex theorem for hyperbolic polygons},
  journal = {Discrete Math.},
  volume  = {346},
  number  = {7},
  year    = {2023},
  pages   = {113371},
  doi     = {10.1016/j.disc.2023.113371},
  note    = {\url{https://doi.org/10.1016/j.disc.2023.113371}; \href{https://arxiv.org/abs/2302.04159}{arXiv:2302.04159}},
}

@misc{Pacitti2024,
  author = {Pacitti Gentil, Samuel},
  title  = {New four-vertex type theorems for spherical polygons},
  year   = {2024},
  note    = {\href{https://arxiv.org/abs/2404.08077}{arXiv:2404.08077}},
}

@article{Tabachnikov2024,
  author  = {Tabachnikov, Serge},
  title   = {A four-point theorem: yet another variation on an old theme},
  journal = {Math. Intelligencer},
  volume  = {47},
  number  = {2},
  year    = {2025},
  pages   = {171--175},
  doi     = {10.1007/s00283-024-10399-2},
  note    = {\url{https://doi.org/10.1007/s00283-024-10399-2}; \href{https://arxiv.org/abs/2409.12609}{arXiv:2409.12609}},
}

@misc{GluckLean,
  author = {Josefsson, Kristoffer},
  title  = {Lean formalization of converse four-vertex theorems},
  year   = {2026},
  note    = {\url{https://github.com/kejace/cd4vt}},
}

@book{OvsienkoTabachnikov2005,
  author    = {Ovsienko, Valentin and Tabachnikov, Serge},
  title     = {Projective Differential Geometry Old and New},
  series    = {Cambridge Tracts in Mathematics},
  volume    = {165},
  publisher = {Cambridge University Press},
  year      = {2005},
  doi       = {10.1017/CBO9780511543142},
  note    = {\url{https://doi.org/10.1017/CBO9780511543142}},
}