Xiaonan Liu

	Postdoctoral Scholar (2023-present) Department of Mathematics Vanderbilt University, Nashville, TN, US Ph.D. Mathematics (2019-2023) School of Mathematics Georgia Institute of Technology, Atlanta, GA, US B.Sc. Mathematics (2015-2019) School of Mathematical Sciences University of Science and Technology of China Email: xiaonan.liu@vanderbilt.edu Office: SC1515

About me

I am currently a postdoctoral scholar in the Department of Mathematics at Vanderbilt University, supervised by Professor Mark Ellingham. I received my PhD in Mathematics from Georgia Institute of technology under the supervision of Professor Xingxing Yu. I did my undergraduate study at University of Science and Technology of China (USTC) mentored by Professor Xinmin Hou.

My research interests are structural graph theory, extremal combinatorics, graph coloring and applications in data science and theoretical computer science.

Reseach Papers

Preprints

• On the size of outerplanar graphs with positive Lin-Lu-Yau Ricci curvature (with L. Lu and Z. Wang)
         arXiv:2409.13666.

• On tight (k,l)-stable graphs (with Z. Song and Z. Wang)
         arXiv:2404.01639.

• A tight bound on {C₃, C₅}-free connected graphs with positive Lin-Lu-Yau Ricci curvature (with K. Gamlath, L. Lu, and X. Yuan)
         arXiv:2312.16593.

• On the oriented diameter of near planar triangulations (with Y. Ge and Z. Wang)
         arXiv:2312.03258.

Publications

• Reconstruction and edge reconstruction of triangle-free graphs (with A. Clifton, R. Mahmoud, and A. Shantanam)
         Discrete Math., 347 (2024) 113753   arXiv:2210.00338.

• Polynomial χ-binding functions for t-broom-free graphs (with J. Schroeder, Z. Wang, and X. Yu)
         J. Combin. Theory Ser. B, 162 (2023) 118--133.   arXiv:2106.08871.

• Planar Turán numbers of cycles: A counterexample (with D. W. Cranston, B. Lidický, and A. Shantanam)
         Electron. J. Combin., 29 (2022) P3.31.   arXiv:2110.02043.

• Hamiltonian paths and cycles in a class of 4-uniform hypergraphs (with G. Liu)
         Graphs Combin., 38(4) (2022) 38:122.   arXiv:2104.05016.

• Counting Hamiltonian cycles in planar triangulations (with Z. Wang and X. Yu)
         J. Combin. Theory Ser. B, 155 (2022) 256--277.   arXiv:2105.07551.

• Number of Hamiltonian cycles in 4-connected planar triangulations (with X. Yu)
         SIAM J. Discrete Math., 35(2) (2021) 1005--1021.   arXiv:2104.04898.