@article{FeketeJordanKaszanitzky,
  author       = {Fekete, Zsolt and Jord{\'a}n, Tibor and Kaszanitzky, Vikt{\'o}ria E.},
  title        = {Rigid Two-Dimensional Frameworks with Two Coincident Points},
  journaltitle = {Graphs and Combinatorics},
  date         = {2015},
  volume       = {31},
  number       = {3},
  pages        = {585--599},
  doi          = {10.1007/s00373-013-1390-0}
}

@article{Whiteley,
  author       = {Whiteley, Walter},
  title        = {Vertex Splitting in Isostatic Frameworks},
  journaltitle = {Structural Topology},
  date         = {1990},
  number       = {16},
  pages        = {23--30},
  url          = {https://hdl.handle.net/2099/1055}
}

@article{ConnellyWhiteley,
  author       = {Connelly, Robert and Whiteley, Walter J.},
  title        = {Global Rigidity: The Effect of Coning},
  journaltitle = {Discrete \& Computational Geometry},
  date         = {2010},
  volume       = {43},
  number       = {4},
  pages        = {717--735},
  doi          = {10.1007/s00454-009-9220-0}
}

@article{CJT,
  author       = {Cruickshank, James and Jackson, Bill and Tanigawa, Shin-ichi},
  title        = {Vertex Splitting, Coincident Realisations, and Global Rigidity of Braced Triangulations},
  journaltitle = {Discrete \& Computational Geometry},
  date         = {2023},
  volume       = {69},
  number       = {1},
  pages        = {192--208},
  doi          = {10.1007/s00454-022-00459-9},
  eprinttype   = {arxiv},
  eprint       = {2002.08680},
  eprintclass  = {math.CO}
}

@article{AsimowRoth,
  author       = {Asimow, L. and Roth, B.},
  title        = {The Rigidity of Graphs},
  journaltitle = {Transactions of the American Mathematical Society},
  date         = {1978},
  volume       = {245},
  pages        = {279--289},
  doi          = {10.1090/S0002-9947-1978-0511410-9}
}

@article{Connelly,
  author       = {Connelly, Robert},
  title        = {Generic Global Rigidity},
  journaltitle = {Discrete \& Computational Geometry},
  date         = {2005},
  volume       = {33},
  number       = {4},
  pages        = {549--563},
  doi          = {10.1007/s00454-004-1124-4}
}

@article{GHT,
  author       = {Gortler, Steven J. and Healy, Alexander D. and Thurston, Dylan P.},
  title        = {Characterizing Generic Global Rigidity},
  journaltitle = {American Journal of Mathematics},
  date         = {2010},
  volume       = {132},
  number       = {4},
  pages        = {897--939},
  doi          = {10.1353/ajm.0.0132},
  eprinttype   = {arxiv},
  eprint       = {0710.0926},
  eprintclass  = {math.MG}
}

@article{Hendrickson,
  author       = {Hendrickson, Bruce},
  title        = {Conditions for Unique Graph Realizations},
  journaltitle = {SIAM Journal on Computing},
  date         = {1992},
  volume       = {21},
  number       = {1},
  pages        = {65--84},
  doi          = {10.1137/0221008}
}

% EDIT: Used the journal version verified in sources/TanigawaJordan.pdf and removed the preprint-numbering note.
@article{JordanTanigawa,
  author       = {Jord{\'a}n, Tibor and Tanigawa, Shin-ichi},
  title        = {Global Rigidity of Triangulations with Braces},
  journaltitle = {Journal of Combinatorial Theory, Series B},
  date         = {2019},
  volume       = {136},
  pages        = {249--288},
  doi          = {10.1016/j.jctb.2018.11.003},
  url          = {https://doi.org/10.1016/j.jctb.2018.11.003}
}

@article{JordanSzabadka,
  author       = {Jord{\'a}n, Tibor and Szabadka, Zolt{\'a}n},
  title        = {Operations Preserving the Global Rigidity of Graphs and Frameworks in the Plane},
  journaltitle = {Computational Geometry},
  date         = {2009},
  volume       = {42},
  number       = {6--7},
  pages        = {511--521},
  doi          = {10.1016/j.comgeo.2008.09.007}
}

% EDIT: Added the recent partial results and survey discussed in the revised introduction.
@article{CJTManifolds,
  author       = {Cruickshank, James and Jackson, Bill and Tanigawa, Shin-ichi},
  title        = {Global Rigidity of Triangulated Manifolds},
  journaltitle = {Advances in Mathematics},
  date         = {2024},
  volume       = {458},
  eid          = {109953},
  doi          = {10.1016/j.aim.2024.109953},
  eprinttype   = {arxiv},
  eprint       = {2204.02503},
  eprintclass  = {math.CO}
}

% EDIT: Replaced the survey preprint citation with its verified published 2026 Cambridge chapter, retaining the arXiv identifier.
@incollection{CJJTSurvey,
  author       = {Cruickshank, James and Jackson, Bill and Jord{\'a}n, Tibor and Tanigawa, Shin-ichi},
  title        = {Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach},
  booktitle    = {Surveys in Combinatorics 2026},
  editor       = {Gagarin, Andrei and Behrend, Roger and Lettington, Matthew and Aliev, Iskander},
  series       = {London Mathematical Society Lecture Note Series},
  number       = {505},
  publisher    = {Cambridge University Press},
  date         = {2026},
  pages        = {189--230},
  doi          = {10.1017/9781009766012.007},
  eprinttype   = {arxiv},
  eprint       = {2508.11636},
  eprintclass  = {math.HO}
}