# Research

My research interests include extremal combinatorics, probabilistic/algebraic methods, spectral graph theory, structural graph theory, and theoretical computer science.

Below is a list of my publications and preprints:

- A counterexample to the Alon-Saks-Seymour conjecture and related problems (with B. Sudakov),
*Combinatorica*32 (2012), 205-219. - Bandwidth theorem for random graphs (with C. Lee and B. Sudakov),
*Journal of Combinatorial Theory, Series B*102 (2012), 14-37. - Quasi-randomness of graph balanced cut properties (with C. Lee),
*Random Structures & Algorithms*, 41 (2012), 124-145. - Nonnegative k-sums, fractional covers, and probability of small deviations (with N. Alon and B. Sudakov),
*Journal of Combinatorial Theory, Series B*, 102 (2012), 784-796. - Large matchings in uniform hypergraphs and the conjectures of Erdos and Samuels (with N. Alon, P. Frankl, V. Rodl, A. Rucinski, and B. Sudakov),
*Journal of Combinatorial Theory, Series A*, 119 (2012), 1200-1215. - The size of a hypergraph and its matching number (with P. Loh, B. Sudakov),
*Combinatorics, Probability and Computing*, 21 (2012), 442-450. - Large feedback arc sets, high minimum degree subgraphs, and long cycles in Eulerian digraphs (with J. Ma, A. Shapira, B. Sudakov, and R. Yuster),
*Combinatorics, Probability and Computing*, 22 (2013), 859-873. - A problem of Erdos on the minimum number of k-cliques (with S. Das, J. Ma, H. Naves, and B. Sudakov),
*Journal of Combinatorial Theory, Series B*, 103 (2013), 344-373. - On the 3-local profiles of graphs (with N. Linial, H. Naves, Y. Peled, and B. Sudakov),
*J. Graph Theory*, 76 (2014), 236-248. - On the maximum induced density of directed stars and related problems,
*SIAM Journal on Discrete Mathematics*, 28-1 (2014), 92-98. - The minimum number of nonnegative edges in hypergraphs (with B. Sudakov),
*The Electronic Journal of Combinatorics*, 21(3) (2014), P3.7. - Maximizing the number of nonnegative subsets (with N. Alon, H. Aydinian),
*SIAM Journal on Discrete Mathematics*, 28-2 (2014), 811-816. - Large supports are required for well-supported Nash equilibria (with Y. Anbalagan, S. Lovett, S. Norin, A. Vetta, and H. Wu),
*Proceedings of 18th on Approximation Algorithms for Combinatorial Optimization Problems (APPROX)*, 2015. - On the densities of cliques and independent sets in graphs (with N. Linial, H. Naves, Y. Peled, and B. Sudakov),
*Combinatorica*36(5) (2016), 493-512. - More on the bipartite decomposition of random graphs (with N. Alon, T. Bohman),
*Journal of Graph Theory*, 84(1) (2017), 45-52. - On graphs decomposable into induced matchings of linear sizes (with J. Fox, B. Sudakov),
*Bull. London Math. Soc.,*49(1) (2017), 45-57. - Degree versions of the Erdos-Ko-Rado Theorem and Erdos hypergraph matching conjecture (with Y. Zhao),
*Journal of Combinatorial Theory, Series A*, 150 (2017) 233-247. - A degree version of the Hilton-Milner Theorem (with P. Frankl, J. Han and Y. Zhao),
*Journal of Combinatorial Theory, Series A*, 155 (2018), 493-502. - On tight cycles in hypergraphs (with J. Ma),
*SIAM Journal on Discrete Mathematics*, 33-1 (2019), 230-237. - Two extremal problems on intersecting families,
*European Journal of Combinatorics*, 76 (2019), 1-9. - Rainbow matchings in properly-colored hypergraphs (with T. Li, G. Wang),
*The Electronic Journal of Combinatorics*, 26(1) (2019), P1.4. - Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture,
*Annals of Mathematics*, 190 (2019), 949-955. - On subsets of the hypercube with prescribed Hamming distances (with O. Klurman, C. Pohoata),
*Journal of Combinatorial Theory, Series A*, 171 (2020), Article 105156. - On almost k-covers of hypercubes (with A. Clifton),
*Combinatorica*40 (2020), 511-526. - On local Turan problems (with P. Frankl and V. Rodl),
*Journal of Combinatorial Theory, Series A*, 177 (2021), Article 105329. - Successive vertex orderings of fully regular graphs (with L. Fang, J. Pach, G. Tardos, and J. Zuo),
*Journal of Combinatorial Theory, Series A*, 199 (2023), Article 105776. - Sharing tea on a graph (with J. Gollin, K. Hendrey, T. Huynh, B. Mohar, S. Oum, N. Yang, W. Yu, X. Zhu), submitted.
- On a d-degree Erdos-Ko-Rado theorem (with Y. Zhang), submitted.

Manuscripts not for publication:

- Deterministic bootstrap percolation in high dimensional grids (with C. Lee).
- A note on the double-critical graph conjecture (with A. Yu).
- A non-uniform extension of Baranyai’s Theorem (with Jinye He and Jie Ma).

Below is a list of my coauthors:

Noga Alon, Y. Anbalagan, Harout Aydinian, Tom Bohman, Alexander Clifton, Shagnik Das, Lixing Fang, Jacob Fox, Peter Frankl, Jie Han, Jinye He, Oleksiy Klurman, Choongbum Lee, Tong Li, Nati Linial, Po-Shen Loh, Shachar Lovett, Jie Ma, Humberto Naves, Sergey Norin, Janos Pach, Yuval Peled, Cosmin Pohoata, Vojtech Rodl, Andrzej Rucinski, Asaf Shapira, Benny Sudakov, Gabor Tardos, Adrian Vetta, Guanghui Wang, Hehui Wu, Alexander Yu, Raphy Yuster, Yi Zhao, Junchi Zuo.