Research – Zixiang Xu’s homepage

Frequent collaborators:

Every one of my collaborators is exceptionally talented, and I feel fortunate to learn from them and explore fascinating mathematics together.

Gennian Ge (15), Hong Liu (6), Xinbu Cheng (5), Chi Hoi Yip (5), Tao Zhang (4), Jun Gao (3), Jiangdong Ai (2), Xinqi Huang (2), Yifan Jing (2), Mingyuan Rong (2), Shengtong Zhang (2), Xiaochen Zhao (2), Domagoj Bradač (1), Ting-Wei Chao (1), Oliver Janzer (1), Minqian Liu (1), Chong Shangguan (1), Jozef Skokan (1), Meiqin Wang (1), Zhuo Wu (1), Min Xu (1), Xin Yan (1), Wenjun Yu (1), Xiande Zhang (1), Yijun Zhang (1), Yiwei Zhang (1), Yixuan Zhang (1), Qiang Zhou (1), Moshe Schwartz (0), Yubo Sun (0), Jian Wang (0), Hao Wang (0)

P.S. Marking (0) indicates that we have a collaborative project nearing completion.

PIR, upcoming
Optimal reconstruction codes with given reads, upcoming
Optimal redundancy of function-correcting codes, with Gennian Ge, Xiande Zhang and Yijun Zhang, arxiv:2502.16983
Interpolating chromatic and homomorphism thresholds, with Xinqi Huang, Hong Liu, and Mingyuan Rong, arxiv:2502.09576 (Note on C_{7}-free graphs )
Uniform set systems with small VC-dimension, with Ting-Wei Chao, Chi Hoi Yip, and Shengtong Zhang, arxiv:2501.13850
Strong Ramsey games on two boards, with Jiangdong Ai, Jun Gao and Xin Yan, arxiv:2501.06830
The Frankl-Pach upper bound is not tight for any uniformity, with Gennian Ge, Chi Hoi Yip, Shengtong Zhang and Xiaochen Zhao, arxiv:2412.11901
Algebraic approach to stability results for Erdos-Ko-Rado theorem, with Gennian Ge and Xiaochen Zhao, arxiv:2410.22676
Clique density vs blowups, with Domagoj Bradač, Hong Liu and Zhuo Wu, arxiv:2410.07098
Sublinear hitting sets for some geometric graphs, with Xinbu Cheng, Xinqi Huang and Mingyuan Rong, arxiv:2404.10379.
Beyond chromatic threshold via (p,q)-theorem, and sharp blow-up phenomenon, with Hong Liu, Chong Shangguan and Jozef Skokan, arxiv:2403.17910. (Second proof of main result via regularity) (Extended abstract will appear in SoCG2024)
A new variant of the Erdős–Gyárfás problem on K_5 with Gennian Ge and Yixuan Zhang, arxiv:2306.14682
Intersective sets over abelian groups, with Chi Hoi Yip. arXiv:2207.00053

Sperner systems with restricted differences, with Chi Hoi Yip, arxiv:2210.02409, to appear
Bollobás-Erdős-Tuza conjecture for graphs with no induced Ks,t, with Xinbu Cheng, arxiv:2405.18264, Journal of Graph Theory, to appear
Euclidean Gallai-Ramsey for various configurations, with Xinbu Cheng, arxiv:2305.18218, Discrete & Computational Geometry, to appear
Extremal number of graphs from geometric shapes, with Jun Gao, Oliver Janzer and Hong Liu, arxiv:2303.13380 (Extended abstract will appear in EuroComb23 ), Israel Journal of Mathematics, to appear
A polynomial resultant approach to algebraic construction of extremal graphs, with Tao Zhang and Gennian Ge. arXiv:2109.15148, Science China Mathematics, Volume 68, pages 485–506, (2025)
Piercing independent sets in graphs without large induced matching, with Jiangdong Ai, Hong Liu and Qiang Zhou, arxiv: 2403.19737, Electronic Journal of Combinatorics. 32 (2025), no. 1, Paper No. 1.10.

A rainbow framework for coded caching and its applications, with Min Xu, Gennian Ge and Minqian Liu. arXiv: 2209.04647, IEEE Transactions on Information Theory, vol. 70, no. 3, pp. 1738-1752, March 2024
Exact values and improved bounds on k-neighborly families of boxes, with Xinbu Cheng, Meiqin Wang and Chi Hoi Yip, arxiv: 2301.06485, European Journal of Combinatorics, Volume 118, May 2024, 103926
Local rainbow coloring for various graphs, with Xinbu Cheng. arXiv:2207.07532, Electronic Journal of Combinatorics. 31 (2024), no. 2, Paper No. 2.55.

Embedding bipartite distance graphs under Hamming metric in finite fields, with Wenjun Yu and Gennian Ge. J. Combin. Theory Ser. A 198 (2023), Paper No. 105765
Stability through non-shadows, with Jun Gao and Hong Liu, arxiv:2212.07821, Combinatorica, volume 43, pages 1125–1137 (2023)

On vertex-induced weighted Turán problems, with Yifan Jing and Gennian Ge. Discrete Mathematics 345 (1), 112628, 2022
On color isomorphic subdivisions, with Gennian Ge. Discrete Mathematics 345 (5), 112805, 2022
A note on multicolor Ramsey number of small odd cycles versus a large clique, with Gennian Ge. Discrete Mathematics 345 (6), 112823, 2022
Some extremal results on hypergraph Turán problems, with Tao Zhang and Gennian Ge. Science China Mathematics 65 (8), 1765-1774, 2022

Some tight lower bounds for Turán problems via constructions of multi-hypergraphs, with Tao Zhang and Gennian Ge. European Journal of Combinatorics 89, 103161, 2020
Color isomorphic even cycles and a related Ramsey problem, with Tao Zhang, Yifan Jing and Gennian Ge. SIAM Journal on Discrete Mathematics 34 (3), 1999-2008, 2020
Erdös–Falconer Distance Problem under Hamming Metric in Vector Spaces over Finite Fields, with Gennian Ge. SIAM Journal on Discrete Mathematics 34 (4), 2208-2220, 2020

New theoretical bounds and constructions of permutation codes under block permutation metric, with Yiwei Zhang and Gennian Ge. Designs, Codes and Cryptography 87 (11), 2625-2637, 2019

Sparse universal graph for graphs with bounded edge-vertex ratio, with Xinbu Cheng and Danni Peng. (The main result is worse than that in the second version of a recent paper, see https://arxiv.org/pdf/2311.05500.pdf . Therefore we decided that we will not submit our draft )