@article{chalermsook_approximating_2024,
	title = {Approximating {Sparsest} {Cut} in {Low}-{Treewidth} {Graphs} via {Combinatorial} {Diameter}},
	volume = {20},
	issn = {1549-6325, 1549-6333},
	url = {http://arxiv.org/abs/2111.06299},
	doi = {10.1145/3632623},
	number = {1},
	urldate = {2025-05-07},
	journal = {ACM Transactions on Algorithms},
	author = {Chalermsook, Parinya and Kaul, Matthias and Mnich, Matthias and Spoerhase, Joachim and Uniyal, Sumedha and Vaz, Daniel},
	month = jan,
	year = {2024},
	note = {arXiv:2111.06299 [cs]},
	keywords = {Computer Science - Data Structures and Algorithms},
	pages = {1--20},
	annote = {Comment: 15 pages, 3 figures},
}
@misc{sparsest_cut_notes,
  author       = {Chekuri, Chandra},
  title        = {Introduction to Sparsest Cut},
  howpublished = {Lecture notes, UIUC CS 598CSC: Topics in Graph Algorithms},
  year         = {2024},
  note         = {Accessed on May 9, 2025},
  url          = {https://courses.grainger.illinois.edu/cs598csc/fa2024/Notes/lec-sparsest-cut.pdf}
}

@article{hoory_expander_2006,
	title = {Expander graphs and their applications},
	volume = {43},
	issn = {0273-0979},
	url = {http://www.ams.org/journal-getitem?pii=S0273-0979-06-01126-8},
	doi = {10.1090/S0273-0979-06-01126-8},
	language = {en},
	number = {04},
	urldate = {2025-05-09},
	journal = {Bulletin of the American Mathematical Society},
	author = {Hoory, Shlomo and Linial, Nathan and Wigderson, Avi},
	month = aug,
	year = {2006},
	pages = {439--562},
}

@article{arora_osqrtlogn_2010,
	title = {\${O}({\textbackslash}sqrt\{{\textbackslash}logn\})\$ {Approximation} to {SPARSEST} {CUT} in \${\textbackslash}tilde\{{O}\}(n{\textasciicircum}2)\$ {Time}},
	volume = {39},
	issn = {0097-5397, 1095-7111},
	url = {http://epubs.siam.org/doi/10.1137/080731049},
	doi = {10.1137/080731049},
	language = {en},
	number = {5},
	urldate = {2025-05-09},
	journal = {SIAM Journal on Computing},
	author = {Arora, Sanjeev and Hazan, Elad and Kale, Satyen},
	month = jan,
	year = {2010},
	pages = {1748--1771},
}

@misc{dorsi2024sparsestcuteigenvaluemultiplicities,
      title={Sparsest cut and eigenvalue multiplicities on low degree Abelian Cayley graphs}, 
      author={Tommaso d'Orsi and Chris Jones and Jake Ruotolo and Salil Vadhan and Jiyu Zhang},
      year={2024},
      eprint={2412.17115},
      archivePrefix={arXiv},
      primaryClass={cs.DS},
      url={https://arxiv.org/abs/2412.17115}, 
}

@inproceedings{arora_expander_2004,
	address = {New York, NY, USA},
	series = {{STOC} '04},
	title = {Expander flows, geometric embeddings and graph partitioning},
	isbn = {978-1-58113-852-8},
	url = {https://doi.org/10.1145/1007352.1007355},
	doi = {10.1145/1007352.1007355},
	abstract = {We give a O(√log n)-approximation algorithm for sparsest cut, balanced separator, and graph conductance problems. This improves the O(log n)-approximation of Leighton and Rao (1988). We use a well-known semidefinite relaxation with triangle inequality constraints. Central to our analysis is a geometric theorem about projections of point sets in Rd, whose proof makes essential use of a phenomenon called measure concentration. We also describe an interesting and natural "certificate" for a graph's expansion, by embedding an n-node expander in it with appropriate dilation and congestion. We call this an expander flow.},
	urldate = {2025-05-09},
	booktitle = {Proceedings of the thirty-sixth annual {ACM} symposium on {Theory} of computing},
	publisher = {Association for Computing Machinery},
	author = {Arora, Sanjeev and Rao, Satish and Vazirani, Umesh},
	month = jun,
	year = {2004},
	pages = {222--231},
	file = {Submitted Version:/Users/congyu/Zotero/storage/GALRKD2A/Arora et al. - 2004 - Expander flows, geometric embeddings and graph partitioning.pdf:application/pdf},
}

@article{leighton_multicommodity_1999,
	title = {Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms},
	volume = {46},
	issn = {0004-5411},
	url = {https://dl.acm.org/doi/10.1145/331524.331526},
	doi = {10.1145/331524.331526},
	number = {6},
	urldate = {2025-05-09},
	journal = {J. ACM},
	author = {Leighton, Tom and Rao, Satish},
	month = nov,
	year = {1999},
	pages = {787--832},
	file = {Full Text PDF:/Users/congyu/Zotero/storage/EVDSDZAH/Leighton and Rao - 1999 - Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms.pdf:application/pdf},
}