Welcome!

I'm Jie Han, a combinatorist with interests mainly on extremal combinatorics, graph theory and theoretical computer science. I'm a professor at School of Mathematics and Statistics, Beijing Institute of Technology since 2022.

Postdoc Positions: 2-year postdoc positions with one year extension. Please send your inquiry and CV by email.

Email: lastname.firstname@bit.edu.cn

PhD. 2015. Perfect Matchings, Tilings and Hamilton Cycles in Hypergraphs. Georgia State University. Supervisor: Yi Zhao.

Past positions

• Senior Researcher, 2020-2022, Theory Lab, Huawei Hong Kong Research Center.
• Assistant Professor, 2018-2020, Department of Mathematics, University of Rhode Island, RI, USA.
• Postdoc research fellow, 2015-2018, Universidade de Sao Paulo. Mentor: Yoshiharu Kohayakawa.
• Postdoc research fellow, 2015-2016, University of Birmingham. Mentor: Deryk Osthus.

Coauthors

Josefran O. Bastos, Fabricio Benevides, Wiebke Bedenknecht, Julia Böttcher, Yulin Chang (4), Guantao Chen, Yangyang Cheng (2), Louis DeBiasio, Laihao Ding(2), Asaf Ferber(2), Peter Frankl, Luyining Gan (5), Wei Gao (3), Huifen Ge, Hiep Han(2), Jie Hu(3), Ping Hu, Hao Huang, Matthew Jenssen, Peter Keevash, Jaehoon Kim(2), Yoshiharu Kohayakawa (12👑), Shoham Letzter, Allan Lo (2), Dingjia Mao(2), Richard Montgomery, Patrick Morris(6), Guilherme Oliveira Mota(4), Suil O, Olaf Parczyk(2), Yury Person(4), Joanna Polycn, Barnaby Roberts, Andrzej Rucinski, Marcelo T. Sales(2), Nicolás Sanhueza-Matamala, Songling Shan, Xichao Shu(2), Henrique Stagni(2), Lin Sun(4), Shumin Sun(2), Lubos Thoma, Andrew Treglown (3), Shoichi Tsuchiya, Roman Vershynin, Bin Wang (2), Guanghui Wang(16👑), Xiaofan Yuan, Donglei Yang (9), Chuanyun Zang (2), Yi Zhao (14👑), Wenling Zhou(2).

Selected Papers

• On rainbow thresholds, with Xiaofan Yuan, RS&A, accepted.
  Resolving a recent problem of Bell, Frieze, and Marbach, we establish the threshold result of Frankston--Kahn--Narayanan--Park in the rainbow setting. Our result provides applications to the thresholds for rainbow structures in randomly colored random graphs.


• The decision problem for perfect matchings in dense hypergraphs, with Luyining Gan, ICALP 2022, paper 64, 1-16.
  We study a conjecture of Keevash-Knox-Mycroft [STOC '13 & Adv. Math. '15] on the decision problem for hypergraph perfect matchings under minimum l-degree condition. Our result reduces the problem to the study of perfect fractional matchings and thus resolves the algorithmic aspect of the decision problem. As a corollary, we resolve the conjecture for l≥0.4k.


• F-factors in quasirandom hypergraphs, with Laihao Ding, Shumin Sun, Guanghui Wang and Wenling Zhou, JLMS, 106(2022), No. 3, 1810-1843.
  We study the following problem of Lenz and Mubayi: which k-uniform hypergraph F can be perfectly tiled in a sufficiently large linear quasi-random k-uniform hypergraph with a minimum degree condition (assuming the obvious divisibility constraint)? We show that this F-factor problem can be reduced to an F-cover problem, and give a solution to the case k=3.


• Non-linear Hamilton cycles in linear quasi-random hypergraphs, with Xichao Shu and Guanghui Wang. SODA '21, 74-88.
  We solve a problem of Lenz, Mubayi and Mycroft, showing that given l<k such that k-l does not divide k, linear quasi-randomness together with a minimum (l+1)-degree condition guarantees Hamilton l-cycles in k-uniform hypergraphs, while a similar minimum l-degree does not suffice.


• On Perfect Matchings in k-complexes, IMRN, 11(2021), 8741–8762.
  We give new proofs of several characterization theorems for the existence of perfect matchings in dense simplicial complexes by Keevash and Mycroft [Mem. AMS, 2015]. In particular, our proof avoids the use of the hypergraph regularity lemma and the hypergraph blow-up lemma. Instead, we use the lattice-based absorbing method developed by Han and a recent probabilistic argument of Kohayakawa, Person and Han.


• Decision problem for Perfect Matchings in Dense k-uniform Hypergraphs, Trans. AMS, 369-7(2017), 5197-5218.
  We show that the decision problem for the containment of perfect matchings in k-uniform hypergraphs with minimum codegree at least n/k can be solved in polynomial time. This solves a problem of Karpinski, Rucinski and Szymanska completely and improves the work of Keevash, Knox and Mycroft.

List of papers

Preprints on ArXiv

1. Jie Han and Yi Zhao. Turán number of complete multipartite graphs in multipartite graphs.
2. Jie Han, Jie Hu and Donglei Yang. A robust version of the multipartite Hajnal-Szemeredi theorem.
3. Yulin Chang, Jie Han and Lin Sun. The threshold for powers of tight Hamilton cycles in random hypergraphs.
4. Luyining Gan, Jie Han and Jie Hu. An algorithmic version of the Hajnal-Szemerédi theorem.
5. Asaf Ferber, Jie Han and Dingjia Mao. Dirac-type Problem of Rainbow matchings and Hamilton cycles in Random Graphs.
6. Jie Han and Donglei Yang. Spanning trees in sparse expanders.
7. Jie Han, Xichao Shu and Guanghui Wang. Non-linear Hamilton cycles in linear quasirandom and uniformly dense hypergraphs.

Accepted/to appear.

8. Jie Han, Lin Sun and Guanghui Wang. Minimum degree conditions for Hamilton \ell-cycles in k-uniform hypergraphs. Elec. JC, accepted.
9. Asaf Ferber, Jie Han, Dingjia Mao and Roman Vershynin. Hamiltonicity of Sparse Pseudorandom Graphs. CPC, accepted.
10. Jie Han and Xiaofan Yuan. On rainbow thresholds. RS&A, accepted.
11. Yangyang Cheng, Jie Han, Bin Wang, Guanghui Wang and Donglei Yang. Transversal Hamilton cycle in hypergraph systems. SIDMA, accepted.

2024

12. Ming Chen, Jie Han, Yantao Tang, and Donglei Yang. On powers of Hamilton cycles in Ramsey-Turán Theory. SIDMA, 38(2024), No. 3, 2489-2508.
13. Ming Chen, Jie Han, Guanghui Wang and Donglei Yang. H-factors in graphs with small independence number. JCTB, 169(2024), 373-405.
14. Jie Han, Lin Sun and Guanghui Wang. Large Y-tilings in 3-uniform hypergraphs. European JC, 120(2024), 103976.
15. Jie Han, Jie Hu, Lidan Ping, Guanghui Wang, Yi Wang, and Donglei Yang. Spanning trees in graphs without large bipartite holes. CPC, 33-3(2024), 270-285.
16. Jie Han, Patrick Morris, Guanghui Wang and Donglei Yang. A Ramsey--Turan theory for tilings in graphs. RS&A, 64-1(2024), 94-124.

2023

17. Yangyang Cheng, Jie Han, Bin Wang and Guanghui Wang. Rainbow spanning structures in graph and hypergraph systems. Forum of Math, Sigma, Volume 11(2023), e95
18. Luyining Gan, Jie Han, Lin Sun and Guanghui Wang. Large Y-tilings and Hamilton l-cycles in k-uniform hypergraphs. JGT, 104-3(2023), 516-556.
19. Yulin Chang, Jie Han and Lubos Thoma. On powers of tight Hamilton cycles in randomly perturbed hypergraphs., RS&A, 63-3(2023), 591-609.
20. Jie Han, Ping Hu, Guanghui Wang and Donglei Yang. Clique-factors in graphs with sublinear l-independence number. CPC, 32-4(2023), 665-681.
21. Fan Chang, Jie Han, Jaehoon Kim, Guanghui Wang and Donglei Yang. Embedding clique-factors in graphs with low l-independence number, JCTB, 161(2023), 301-330.
22. Laihao Ding, Jie Han, Shumin Sun, Guanghui Wang and Wenling Zhou. Tiling multipartite hypergraphs in Quasi-random Hypergraphs, JCTB, 160(2023), 36-65.

2022

23. Luyining Gan, Wei Gao and Jie Han. On zero-nonzero and sign patterns allowing S_n* or S_n, Linear and Multilinear Algebra, 70(2022)22, 7347-7369.
24. Laihao Ding, Jie Han, Shumin Sun, Guanghui Wang and Wenling Zhou. F-factors in quasirandom hypergraphs, JLMS, 106(2022), No. 3, 1810-1843.
25. Yulin Chang, Huifen Ge, Jie Han and Guanghui Wang. Matchings of given sizes in hypergraphs, SIDMA, 36(2022), No. 3, 2323-2338.
26. Jie Han. Cover 3-uniform hypergraphs by vertex-disjoint tight paths, JGT, 101(2022), No. 4, 782-802.
27. Luyining Gan and Jie Han. The decision problem for perfect matchings in dense hypergraphs, ICALP 2022, paper 64, 1-16.
28. Jie Han and Yi Zhao. Turán number of disjoint triangles in 4-partite graphs, Elec. JC, 29(2), 2022, #P2.35.
29. Jie Han, Tao Guo, Qiaoqiao Zhou, Wei Han, Bo Bai and Gong Zhang. Structural Entropy of the Stochastic Block Models. Entropy 2022, 24(1), 81.
30. Yulin Chang, Jie Han, Yoshiharu Kohayakawa, Patrick Morris and Guilherme O. Mota. Factors in randomly perturbed hypergraphs. RS&A, 60(2022), 153-165.
31. Hiep Han, Jie Han and Yi Zhao. Minimum degree thresholds for Hamilton (k/2)-cycles in k-uniform hypergraphs. JCTB, 153(2022), 105-148.
32. Luyining Gan and Jie Han. Hamiltonicity in Cherry-quasirandom 3-graphs. European JC, 102(2022)103457.

2021

33. Jie Han, Yoshiharu Kohayakawa, and Yury Person. Near-perfect clique-factors in sparse pseudorandom graphs CPC, 30(2021), 570-590. An extended abstract of this paper appears in the Proceedings of Discrete Mathematics Days 2018 (Sevilla).
34. Longlong Li, Hu Chen, Ping Li, Jie Han, Guanghui Wang and Gong Zhang. The K-Core Decomposition Algorithm Under the Framework of GraphBLAS, HPEC 2021.
35. Jie Han, Joanna Polycn and Andrzej Ruciński. Turán and Ramsey numbers for 3-uniform minimal paths of length 4. JGT, 98(2021), No. 3, 460-498.
36. Jie Han, Yoshiharu Kohayakawa, Shoham Letzter, Guilherme O. Mota and Olaf Parczyk. The size-Ramsey number of 3-uniform tight paths. Advances in Combinatorics, 2021:5, 12 pp.
37. Jie Han. On perfect matchings in k-complexes IMRN, 11(2021), 8741–8762.
38. Jie Han, Allan Lo and Nicolás Sanhueza-Matamala. Covering and tiling hypergraphs with tight cycles CPC, 30(2021), 288-329. An extended abstract of this paper appeared in Eurocomb '17.
39. Jie Han, Patrick Morris and Andrew Treglown. Tilings in randomly perturbed graphs: bridging the gap between Hajnal--Szemerédi and Johansson--Kahn--Vu. RS&A, 58 (2021) 480-516.
40. Jie Han, Yoshiharu Kohayakawa, Patrick Morris, and Yury Person. Finding any given 2-factor in sparse pseudorandom graphs efficiently. JGT, 96(2021), no. 1, Special issue: Ron Graham, 87-108.
41. Jie Han, Xichao Shu and Guanghui Wang. Non-linear Hamilton cycles in linear quasi-random hypergraphs. SODA 2021, 74-88.

    2020

42. Jie Han, Chuanyun Zang and Yi Zhao. Matchings in k-partite k-uniform hypergraphs JGT, 95(2020), no. 1, 34-58.
43. Jie Han, Matthew Jenssen, Yoshiharu Kohayakawa, Guilherme Oliveira Mota, and Barnaby Roberts. The multicolour size-Ramsey number of powers of paths. JCTB, 145(2020), 359-375.
44. Josefran de Oliveira Bastos, Fabricio S. Benevides, and Jie Han. The number of Gallai k-colorings of complete graphs. JCTB, 144(2020), 1-13.
45. Jie Han and Yi Zhao. Hamiltonicity in randomly perturbed hypergraphs JCTB, 144(2020), 14-31.
46. Jie Han and Peter Keevash. Finding perfect matchings in dense hypergraphs. SODA 2020, pp. 2366-2377.
47. Hiep Han, Jie Han, and Patrick Morris. Factors and loose Hamilton cycles in sparse pseudo-random hypergraphs SODA 2020, pp. 702-717. The full version of this paper appears in RS&A, 61 (2022), no. 1, 101-125.
48. Jie Han and Andrew Treglown. The complexity of perfect matchings and packings in dense hypergraphs JCTB, 141(2020), 72-104.

2019

49. Jie Han, Yoshiharu Kohayakawa, Patrick Morris, and Yury Person. Clique-factors in sparse pseudorandom graphs European JC, Volume 82 (December 2019) 102999.
50. Wiebke Bedenknecht, Jie Han, Yoshiharu Kohayakawa, and Guilherme O. Mota. Powers of tight Hamilton cycles in randomly perturbed hypergraphs RS&A, 55-4(2019) 795-807.
51. Julia Böttcher, Jie Han, Yoshiharu Kohayakawa, Richard Montgomery, Olaf Parczyk and Yury Person. Universality for bounded degree spanning trees in randomly perturbed graphs RS&A, 55-4(2019) 854-864.
52. Wei Gao, Jie Han and Yi Zhao. Codegree conditions for tiling complete k-partite k-graphs and loose cycles CPC, 28-6 (2019) 840-870.
53. Jie Han, Yoshiharu Kohayakawa, Marcelo Tadeu Sales and Henrique Stagni. Extremal and probabilistic results for order types. SODA 2019, pp 426-435.

2018

54. Jie Han, Yoshiharu Kohayakawa, Marcelo Tadeu Sales, and Henrique Stagni. Property testing for point sets on the plane. LATIN 2018. LNCS, vol 10807, 584-596.
55. Jie Han. On vertex-disjoint paths in regular graphs Elec. JC, 25-2(2018), P2.12.
56. Jie Han. On perfect matchings and tilings in uniform hypergraphs SIDMA, 32-2 (2018), 919–932.
57. Peter Frankl, Jie Han, Hao Huang and Yi Zhao. A degree version of the Hilton--Milner Theorem, JCTA, 155(2018) 493-502.
58. Jie Han and Yoshiharu Kohayakawa. On hypergraphs without loose cycles, Discrete Math, 341-4(2018) 946-949.
59. Jie Han and Jaehoon Kim. Two-regular subgraphs of odd-uniform hypergraphs, JCTB, 128(2018) 175-191.

2017

60. Guantao Chen, Jie Han, Suil O, Songling Shan, and Shoichi Tsuchiya. Forbidden pairs and the existence of a spanning Halin subgraph. Graphs and Combin., 33-5(2017) 1321-1345.
61. Jie Han, Allan Lo, Andrew Treglown and Yi Zhao. Exact minimum codegree threshold for K^-_4-factors CPC, 26-6(2017) 856-885.
62. Wei Gao and Jie Han. Minimum codegree threshold for C_6^3-factors in 3-uniform hypergraphs. CPC, 26-4 (2017) 536-559.
63. Jie Han. The complexity of perfect packings in dense graphs. TAMC 2017. LNCS, vol 10185.
64. Jie Han. Decision problem for Perfect Matchings in Dense k-uniform Hypergraphs Transactions of the AMS, 369-7(2017), 5197-5218.
65. Jie Han, Chuanyun Zang and Yi Zhao. Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs JCTA, 149(2017) 115-147.
66. Jie Han and Yoshiharu Kohayakawa. The maximum size of a non-trivial intersecting uniform family that is not a subfamily of the Hilton-Milner family Proceedings of the AMS, 145-1(2017) 73–87.

2016

67. Jie Han. Near perfect matchings in k-uniform hypergraphs II SIDMA 30-3 (2016) 1453-1469.
68. Jie Han. Perfect matchings in hypergraphs and the Erdos Matching Conjecture SIDMA 30-3 (2016) 1351-1357.
69. Jie Han and Yi Zhao. Forbidding Hamilton cycles in uniform hypergraphs JCTA, 143 (2016) 107–115.

2015

70. Jie Han and Yi Zhao. Minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs JCTA, 132 (2015) 194-223.
71. Jie Han. Near perfect matchings k-uniform hypergraphs CPC 24 (2015), no. 5, 723-732.
72. Jie Han and Yi Zhao. Minimum vertex degree threshold for C_4^3-tiling JGT, 79 (2015), no. 4, 300-317.
73. Jie Han and Yi Zhao. Minimum vertex degree threshold for loose Hamilton cycles in 3-uniform hypergraphs JCTB, 114 (2015) 70-96.

2013

74. Jie Han and Yi Zhao. On multipartite Hajnal-Szemeredi theorems Discrete Math, 313-10(2013) 1119-1129.

PhD thesis. Perfect Matchings, Tilings, Hamilton Cycles in Hypergraphs. Georgia State University, May 2015.