Publications

Preprints

67. Optimal bounds on the polynomial Schur’s theorem, 24 pages.
    with Jaehoon Kim, Péter Pál Pach
    
68. Piercing independent sets in graphs without large induced matching, 3 pages.
    with Jiangdong Ai, Zixiang Xu, Qiang Zhou
    
69. Beyond chromatic threshold via $(p,q)$-theorem, and sharp blow-up phenomenon, 23 pages. An extended abstract of this paper appears in SOCG 2024. 
    with Chong Shangguan, Jozef Skokan, Zixiang Xu
    
70. Generalized Ramsey–Turán density for cliques, 28 pages.
    with Jun Gao, Suyun Jiang, Maya Sankar
    
71. Graph with any rational density and no rich subsets of linear size, 10 pages.
    with Seonghyuk Im, Suyun Jiang, Tuan Tran
    
72. Extremal density for subdivisions with length or sparsity constraints, 34 pages.
    with Jaehoon Kim, Yantao Tang, Guanghui Wang, Donglei Yang, Fan Yang
    
73. Vanishing codegree Turán density implies vanishing uniform Turán density, 10 pages.
    with Laihao Ding, Shuaichao Wang, Haotian Yang
    
74. Erdős distinct subset sums problem in a modular setting, 10 pages.
    with Stijn Cambie, Jun Gao, Younjin Kim
    
75. A bandwidth theorem for graph transversals, 30 pages.
    with Debsoumya Chakraborti, Seonghyuk Im, Jaehoon Kim
    
76. Geometric constructions for Ramsey-Turán theory, 27 pages.
    with Christian Reiher, Maryam Sharifzadeh, Katherine Staden

To appear

57. New lower bounds on kissing numbers and spherical codes in high dimensions, 20 pages.
    with Irene Gil Fernández, Jaehoon Kim, Oleg Pikhurko
    American Journal of Mathematics
58. Crux, space constraints and subdivisions, 37 pages.
    with Seonghyuk Im, Jaehoon Kim, Younjin Kim
    Journal of Combinatorial Theory, Series B
59. How connectivity affects the extremal number of trees, 10 pages.
    with Suyun Jiang, Nika Salia
    Journal of Combinatorial Theory, Series B
60. Rainbow cycles in properly edge-colored graphs, 9 pages.
    with Jaehoon Kim, Joonkyung Lee, Tuan Tran
    Combinatorica
61. Extremal number of graphs from geometric shapes, 23 pages.
    with Jun Gao, Oliver Janzer, Zixiang Xu
    Israel Journal of Mathematics
62. Many Hamiltonian subsets in large graphs with given density, 11 pages.
    with Stijn Cambie, Jun Gao
    Combinatorics, Probability and Computing
63. On a rainbow extremal problem for color-critical graphs,
    with Debsoumya Chakraborti, Jaehoon Kim, Hyunwoo Lee, Jaehyeon Seo
    Random Structures and Algorithms, https://doi.org/10.1002/rsa.21189
64. Stability through non-shadows,
    with Jun Gao, Zixiang Xu
    Combinatorica, https://doi.org/10.1007/s00493-023-00053-4
65. Fractional Helly theorem for Cartesian products of convex sets,
    with Debsoumya Chakraborti, Jaehoon Kim, Jinha Kim, Minki Kim
    Discrete & Computational Geometry, https://doi.org/10.1007/s00454-022-00468-8

2023

48. A solution to Erdős and Hajnal’s odd cycle problem,
    with Richard Montgomery
    Journal of the American Mathematical Society, 36 (2023), 1191-1234, https://doi.org/10.1090/jams/1018
49. Stability from graph symmetrisation arguments with applications to inducibility,
    with Oleg Pikhurko, Maryam Sharifzadeh, Katherine Staden
    Journal of the London Mathematical Society, 108: 1121-1162, 2023, https://doi.org/10.1112/jlms.12777
50. How to build a pillar: a proof of Thomassen’s conjecture,
    with Irene Gil Fernández
    Journal of Combinatorial Theory, Series B, 162 (2023) 13–33, https://doi.org/10.1016/j.jctb.2023.04.004
51. Exponential decay of intersection volume with applications on list–decodability and Gilbert–Varshamov type bound,
    with Jaehoon Kim, Tuan Tran
    IEEE Transactions on Information Theory, vol. 69, no. 5, pp. 2841-2854, 2023, https://doi.org/10.1109/TIT.2022.3232241
52. Disjoint isomorphic balanced clique subdivisions,
    with Irene Gil Fernández, Joseph Hyde, Oleg Pikhurko, Zhuo Wu
    Journal of Combinatorial Theory, Series B, 161 (2023) 417–436, https://doi.org/10.1016/j.jctb.2023.03.002
53. A proof of Frankl’s conjecture on cross-union families,
    with Stijn Cambie, Jaehoon Kim, Tuan Tran
    Combinatorial Theory, 3 (2), 2023, #9, https://doi.org/10.5070/C63261987
54. Ramsey numbers of cycles versus general graphs,
    with John Haslegrave, Joseph Hyde, Jaehoon Kim
    Forum of Mathematics, Sigma, 11:e10 1–18, 2023.
55. Shape of the asymptotic maximum sum-free sets in integer lattice grids,
    with Guanghui Wang, Laurence Wilkies, Donglei Yang
    European Journal of Combinatorics, Volume 107, 103614, 2023.

2022

40. Extremal density for sparse minors and subdivisions,
    with John Haslegrave, Jaehoon Kim
    International Mathematics Research Notices, Volume 2022, Issue 20, 15505–15548, https://doi.org/10.1093/imrn/rnab154
41. Nested cycles with no geometric crossings,
    with Irene Gil Fernández, Jaehoon Kim, Younjin Kim
    Proceedings of the American Mathematical Society, Series B, Volumn 9 (2022), 22-32, https://doi.org/10.1090/bproc/107
42. Polynomial Schur’s theorem,
    with Péter Pál Pach, Csaba Sándor
    Combinatorica, 42, 1357–1384 (2022), https://doi.org/10.1007/s00493-021-4815-z
43. Crux and long cycles in graphs,
    with John Haslegrave, Jie Hu, Jaehoon Kim, Bingyu Luan, Guanghui Wang
    SIAM Journal on Discrete Mathematics, Volume 36, Issue 4, 2022.
44. Clique immersion in graphs without fixed bipartite graph,
    with Guanghui Wang, Donglei Yang
    Journal of Combinatorial Theory, Series B, Volume 157, 346-365, 2022.
45. Well-mixing vertices and almost expanders,
    with Debsoumya Chakraborti, Jaehoon Kim, Jinha Kim, Minki Kim
    Proceedings of the American Mathematical Society, 150, 5097-5110, 2022.

2021

34. The number of maximum primitive sets of integers,
    with Péter Pál Pach, Richárd Palincza
    Combinatorics, Probability and Computing, 30(5), (2021), 781-795.
35. On the rational Turán exponents conjecture,
    with Dongyeap Kang, Jaehoon Kim
    Journal of Combinatorial Theory, Series B, 148, (2021), 149–172.
36. Groups with few maximal sum-free sets,
    with Maryam Sharifzadeh
    Journal of Combinatorial Theory, Series A, 177, (2021), 105333, 18 pages.
37. On the maximum number of integer colourings with forbidden monochromatic sums,
    with Maryam Sharifzadeh, Katherine Staden
    Electronic Journal of Combinatorics, 28 (1), (2021), P1-59, 35 pages.

2020

30. The exact minimum number of triangles in graphs of given order and size,
    with Oleg Pikhurko, Katherine Staden
    Forum of Mathematics, Pi, 8, E8, (2020), 144 pages.
31. Asymptotic structure for the clique density theorem,
    with Jaehoon Kim, Oleg Pikhurko, Maryam Sharifzadeh
    Discrete Analysis, 2020:19, 26 pp.
32. Tree decompositions of graphs without large bipartite holes,
    with Jaehoon Kim, Younjin Kim
    Random Structures and Algorithms, 57 (1), (2020), 150–168.
33. Stability and exact Turán numbers for matroids,
    with Sammy Luo, Peter Nelson, Kazuhiro Nomoto
    Journal of Combinatorial Theory, Series B, 143, (2020), 29–41.

2019

26. The number of multiplicative Sidon sets of integers,
    with Péter Pál Pach
    Journal of Combinatorial Theory, Series A, 165, (2019), 152–175.
27. Edges not in any monochromatic copy of a fixed graph,
    with Oleg Pikhurko, Maryam Sharifzadeh
    Journal of Combinatorial Theory, Series B, 135, (2019), 16–43.
28. Bivariate fluctuations for the number of arithmetic progressions in random sets,
    with Yacine Barhoumi-Andréani, Christoph Koch
    Electronic Journal of Probability, 24 (2019), paper 145, 32 pp.
29. Two conjectures in Ramsey-Turán theory,
    with Jaehoon Kim, Younjin Kim
    SIAM Journal on Discrete Mathematics, 33 (1), (2019), 564–586.
30. A degree sequence Komlós theorem,
    with Joseph Hyde, Andrew Treglown
    SIAM Journal on Discrete Mathematics, 33 (4), (2019), 2041–2061.
31. Structure and supersaturation for intersecting families,
    with József Balogh, Shagnik Das, Maryam Sharifzadeh, Tuan Tran
    Electronic Journal of Combinatorics, 26 (2), (2019), P2.34, 38 pages.

2018

20. Sharp bound on the number of maximal sum-free subsets of integers,
    with József Balogh, Maryam Sharifzadeh, Andrew Treglown
    Journal of the European Mathematical Society, 20 (8), (2018), 1885–1911.
21. Rainbow spanning trees in properly coloured complete graphs,
    with József Balogh, Richard Montgomery
    Discrete Applied Mathematics, 247, (2018), 97–101.

2017

18. Proof of Komlós’s conjecture on Hamiltonian subsets,
    with Jaehoon Kim, Maryam Sharifzadeh, Katherine Staden
    Proceedings of the London Mathematical Society, 115 (5), (2017), 974–1013.
19. A proof of Mader’s conjecture on large clique subdivisions in C_4-free graphs,
    with Richard Montgomery
    Journal of the London Mathematical Society, 95 (1), (2017), 203–222.
20. The number of subsets of integers with no k-term arithmetic progression,
    with József Balogh, Maryam Sharifzadeh
    International Mathematics Research Notices, 20, (2017), 6168–6186.
21. Local conditions for exponentially many subdivisions,
    with Maryam Sharifzadeh, Katherine Staden
    Combinatorics, Probability and Computing, 26 (3), (2017), 423–430.
22. On two problems in Ramsey-Turán theory,
    with József Balogh, Maryam Sharifzadeh
    SIAM Journal on Discrete Mathematics, 31 (3), (2017), 1848–1866.
23. The typical structure of graphs with no large cliques,
    with József Balogh, Neal Bushaw, Maurício Collares Neto, Robert Morris, Maryam Sharifzadeh
    Combinatorica, 37 (4), (2017), 617–632.
24. Densities in large permutations and parameter testing,
    with Roman Glebov, Carlos Hoppen, Tereza Klimošová, Yoshiharu Kohayakawa, Daniel Kráľ
    European Journal of Combinatorics, 60, (2017), 89–-99.

–2015

1. The number of maximal sum-free subsets of integers,
   with József Balogh, Maryam Sharifzadeh, Andrew Treglown
   Proceedings of the American Mathematical Society, 143, (2015), 4713–4721.
2. The typical structure of maximal triangle-free graphs,
   with József Balogh, Šárka Petříčková, Maryam Sharifzadeh
   Forum of Mathematics, Sigma, 3, (2015), 19 pages.
3. Subdivisions of a large clique in C_6-free graphs,
   with József Balogh, Maryam Sharifzadeh
   Journal of Combinatorial Theory, Series B, 112, (2015), 18–35.
4. Intersecting families of discrete structures are typically trivial,
   with József Balogh, Shagnik Das, Michelle Delcourt, Maryam Sharifzadeh
   Journal of Combinatorial Theory, Series A, 132, (2015), 224–245.
5. On the number of K_4-saturating edges,
   with József Balogh
   Journal of Combinatorial Theory, Series B, 109, (2014), 250–257.
6. Multicolor Ramsey numbers for triple systems,
   with Maria Axenovich, András Gyárfás, Dhruv Mubayi
   Discrete Mathematics, 322, (2014) 69–-77.
7. Upper bounds on the size of 4- and 6-cycle-free subgraphs of the hypercube,
   with József Balogh, Ping Hu, Bernard Lidický
   European Journal of Combinatorics, 35, (2014), 75–85.
8. On the Turan number of forests,
   with Bernard Lidický, Cory Palmer
   Electronic Journal of Combinatorics, 20 (2), (2013), paper 62, 14pp.
9. The biased odd cycle game,
   with Asaf Ferber, Roman Glebov, Michael Krivelevich, Cory Palmer, Tomas Valla, Máté Vizer
   Electronic Journal of Combinatorics, 20 (2), (2013), paper 9, 10pp.
10. Extremal graphs for blow-ups of cycles and trees,
    Electronic Journal of Combinatorics, 20 (1), (2013), paper 65, 16pp.
11. Dominating sets in triangulations on surfaces,
    with Michael Pelsmajer
    Ars Math. Contemp., 4, (2011), 177–204.