@article{LLR95,
  author = {Linial, Nathan and London, Eran and Rabinovich, Yuri},
  title = {The geometry of graphs and some of its algorithmic applications},
  journal = {Combinatorica},
  volume = {15},
  number = {2},
  pages = {215--245},
  year = {1995},
  doi = {10.1007/BF01200757},
  url = {https://link.springer.com/article/10.1007/BF01200757}
}

@article{GNRS04,
  author = {Gupta, Anupam and Newman, Ilan and Rabinovich, Yuri and Sinclair, Alistair},
  title = {Cuts, Trees and {$\ell_1$}-Embeddings of Graphs},
  journal = {Combinatorica},
  volume = {24},
  number = {2},
  pages = {233--269},
  year = {2004},
  doi = {10.1007/s00493-004-0015-x},
  url = {https://link.springer.com/article/10.1007/s00493-004-0015-x},
  note = {Preliminary version in FOCS 1999, pp. 399--408}
}

@inproceedings{Rao99,
  author = {Rao, Satish},
  title = {Small distortion and volume preserving embeddings for planar and {Euclidean} metrics},
  booktitle = {Proceedings of the Fifteenth Annual Symposium on Computational Geometry},
  series = {SCG '99},
  pages = {300--306},
  publisher = {ACM},
  year = {1999},
  doi = {10.1145/304893.304983},
  url = {https://doi.org/10.1145/304893.304983}
}

@article{OS81,
  author = {Okamura, Haruko and Seymour, Paul D.},
  title = {Multicommodity flows in planar graphs},
  journal = {Journal of Combinatorial Theory, Series B},
  volume = {31},
  number = {1},
  pages = {75--81},
  year = {1981},
  doi = {10.1016/S0095-8956(81)80012-3},
  url = {https://doi.org/10.1016/S0095-8956(81)80012-3}
}

@inproceedings{CJLV08,
  author = {Chakrabarti, Amit and Jaffe, Alexander and Lee, James R. and Vincent, Justin},
  title = {Embeddings of topological graphs: Lossy invariants, linearization, and 2-sums},
  booktitle = {2008 49th Annual IEEE Symposium on Foundations of Computer Science},
  pages = {761--770},
  publisher = {IEEE Computer Society},
  year = {2008},
  doi = {10.1109/FOCS.2008.79},
  url = {https://www.cs.dartmouth.edu/~ac/Pubs/focs08-planar.pdf}
}

@inproceedings{Sidiropoulos13,
  author = {Sidiropoulos, Anastasios},
  title = {Non-positive curvature and the planar embedding conjecture},
  booktitle = {2013 IEEE 54th Annual Symposium on Foundations of Computer Science},
  pages = {177--186},
  publisher = {IEEE Computer Society},
  year = {2013},
  doi = {10.1109/FOCS.2013.27},
  eprint = {1304.7512},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1304.7512}
}

@article{Filtser25,
  author = {Filtser, Arnold},
  title = {A Face Cover Perspective to {$\ell_1$} Embeddings of Planar Graphs},
  journal = {ACM Transactions on Algorithms},
  volume = {21},
  number = {1},
  pages = {4:1--4:21},
  year = {2025},
  doi = {10.1145/3686800},
  url = {https://doi.org/10.1145/3686800},
  note = {Article 4. Published online November 22, 2024}
}

@article{AR98,
  author = {Aumann, Yonatan and Rabani, Yuval},
  title = {An {$O(\log k)$} Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm},
  journal = {SIAM Journal on Computing},
  volume = {27},
  number = {1},
  pages = {291--301},
  year = {1998},
  doi = {10.1137/S0097539794285983},
  url = {https://doi.org/10.1137/S0097539794285983}
}

@inproceedings{KPR93,
  author = {Klein, Philip N. and Plotkin, Serge A. and Rao, Satish},
  title = {Excluded Minors, Network Decomposition, and Multicommodity Flow},
  booktitle = {Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing},
  pages = {682--690},
  publisher = {ACM},
  year = {1993},
  doi = {10.1145/167088.167261},
  url = {https://doi.org/10.1145/167088.167261}
}

@article{CGNRS06,
  author = {Chekuri, Chandra and Gupta, Anupam and Newman, Ilan and Rabinovich, Yuri and Sinclair, Alistair},
  title = {Embedding {$k$}-Outerplanar Graphs into {$\ell_1$}},
  journal = {SIAM Journal on Discrete Mathematics},
  volume = {20},
  number = {1},
  pages = {119--136},
  year = {2006},
  doi = {10.1137/S0895480102417379},
  url = {https://doi.org/10.1137/S0895480102417379}
}

@article{LR10,
  author = {Lee, James R. and Raghavendra, Prasad},
  title = {Coarse Differentiation and Multi-flows in Planar Graphs},
  journal = {Discrete \& Computational Geometry},
  volume = {43},
  number = {2},
  pages = {346--362},
  year = {2010},
  doi = {10.1007/s00454-009-9172-4},
  url = {https://doi.org/10.1007/s00454-009-9172-4}
}

@article{HST88,
  author = {Hurkens, C. A. J. and Schrijver, Alexander and Tardos, {\'E}va},
  title = {On Fractional Multicommodity Flows and Distance Functions},
  journal = {Discrete Mathematics},
  volume = {73},
  number = {1--2},
  pages = {99--109},
  year = {1988},
  doi = {10.1016/0012-365X(88)90137-9},
  url = {https://doi.org/10.1016/0012-365X(88)90137-9}
}

@inproceedings{LS09,
  author = {Lee, James R. and Sidiropoulos, Anastasios},
  title = {On the Geometry of Graphs with a Forbidden Minor},
  booktitle = {Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing},
  pages = {245--254},
  publisher = {ACM},
  year = {2009},
  doi = {10.1145/1536414.1536450},
  url = {https://doi.org/10.1145/1536414.1536450}
}

@inproceedings{KLR19,
  author = {Krauthgamer, Robert and Lee, James R. and Rika, Havana},
  title = {Flow-Cut Gaps and Face Covers in Planar Graphs},
  booktitle = {Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms},
  pages = {525--534},
  publisher = {SIAM},
  year = {2019},
  doi = {10.1137/1.9781611975482.33},
  url = {https://doi.org/10.1137/1.9781611975482.33}
}

@article{CCN15,
  author = {Chalopin, J{\'e}r{\'e}mie and Chepoi, Victor and Naves, Guyslain},
  title = {Isometric Embedding of {Busemann} Surfaces into {$L_1$}},
  journal = {Discrete \& Computational Geometry},
  volume = {53},
  number = {1},
  pages = {16--37},
  year = {2015},
  doi = {10.1007/s00454-014-9643-0},
  url = {https://doi.org/10.1007/s00454-014-9643-0}
}

@article{Kumar25,
  author = {Kumar, Nikhil},
  title = {An Approximate Generalization of the {Okamura--Seymour} Theorem},
  journal = {SIAM Journal on Computing},
  volume = {54},
  number = {5},
  pages = {FOCS22-159--FOCS22-177},
  year = {2025},
  doi = {10.1137/23M1545938},
  url = {https://doi.org/10.1137/23M1545938}
}

@article{NR03,
  author = {Newman, Ilan and Rabinovich, Yuri},
  title = {A Lower Bound on the Distortion of Embedding Planar Metrics into {Euclidean} Space},
  journal = {Discrete \& Computational Geometry},
  volume = {29},
  number = {1},
  pages = {77--81},
  year = {2003},
  doi = {10.1007/s00454-002-2813-5},
  url = {https://doi.org/10.1007/s00454-002-2813-5}
}

@article{AFGN22,
  author = {Abraham, Ittai and Filtser, Arnold and Gupta, Anupam and Neiman, Ofer},
  title = {Metric Embedding via Shortest Path Decompositions},
  journal = {SIAM Journal on Computing},
  volume = {51},
  number = {2},
  pages = {290--314},
  year = {2022},
  doi = {10.1137/19M1296021},
  url = {https://doi.org/10.1137/19M1296021},
  note = {Corrigendum, 52(5):1319--1320, 2023}
}

@misc{Treewidth108,
  author = {{OpenAI}},
  title = {{$L_1$ Embeddings of Graphs of Bounded Treewidth}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/L1-Embeddings-of-Graphs-of-Bounded-Treewidth-September-23-2026/paper.pdf}{OAI:L1-Embeddings-of-Graphs-of-Bounded-Treewidth-September-23-2026}},
  year = {2026}
}
