I am interested in combinatorics, specifically the coloring of graphs, Ramsey theory, the probabilistic method, and the secretary-type problems.
X. Liu, X. Zhang, Y. Zhang, Every subcubic graph is packing (1,1,2,2,3)-colorable, Discrete Mathematics 348 (11) (2025), 114610.
X. Liu, O. Milenkovic, and G. Moustakides, Query-based selection of optimal candidates under the Mallows model, Theoretical Computer Science 979(2023), 114206.
G. Moustakides, X. Liu, O. Milenkovic, Optimal Stopping Methodology for the Secretary Problem with Random Queries, Journal of Applied Probability (2023), https://doi.org/10.1017/jpr.2023.61.
X. Liu, M. Santana, and T. Short, Every subcubic multigraph is (1,2^7)-packing edge-colorable, Journal of Graph Theory 104 (4) (2023), 851-885.
X. Liu and O. Milenkovic, Finding the second-best candidate under the Mallows model, Theoretical Computer Science 929 (2022), 39-68.
J. Balogh, A. Kostochka, M. Lavrov, and X. Liu, Monochromatic connected matchings in 2-edge-colored multipartite graphs, Journal of Graph Theory, 100 (2022), 578-607.
J. Balogh, A. Kostochka, M. Lavrov, and X. Liu, Monochromatic paths and cycles in 2-edge-colored graphs with large minimum degree, Combinatorics, Probability and Computing 31 (2022) , 109-122.
X. Liu, R. Machado, and O. Milenkovic, Directed intersection representations and the information content of digraphs, IEEE Transactions on Information Theory 67 (1) (2021), 347-357. (Slides)
A. Kostochka and X. Liu, Packing (1,1,2,4)-coloring of subcubic outerplanar graphs, Discrete Applied Mathematics 302 (2021), 8--15. (Slides)
R. Liu, X. Liu, M. Rolek, and G. Yu, Packing (1,1,2,2)-coloring of some subcubic graphs, Discrete Applied Mathematics 283 (2020), 626--630.
J. Balogh, A. Kostochka, M. Lavrov, and X. Liu, Long monochromatic paths and cycles in 2-edge-colored multipartite graphs, Moscow Journal of Combinatorics and Number Theory 9 (1) (2020), 55--100. (slides: 20 mins and 50 mins)
J. Balogh, A. Kostochka, and X. Liu, Cubic graphs with small independence ratio, Electronic Journal of Combinatorics 26 (1) (2019), P1.431. (slides: 20 mins)
J. Balogh, A. Kostochka, and X. Liu, Packing coloring of subdivision of cubic graphs, Graphs and Combinatorics 35 (2) (2019), 513--537. (slides: 20 mins)
J. Balogh, A. Kostochka, and X. Liu, Packing chromatic number of cubic graphs, Discrete Mathematics 341 (2018), 474--483. (slides: 20 mins and 50 mins)
I. Choi and X. Liu, Between proper and square colorings of sparse graphs, https://arxiv.org/pdf/2509.03080.
X. Liu and G. Yu, On the (1^2,2^4)-packing edge-coloring of subcubic graphs, https://arxiv.org/pdf/2402.18353.pdf.
X. Liu and Y. Wang, Partition subcubic planar graphs into independent sets, https://arxiv.org/pdf/2408.12189.pdf.
S. Li, Y. Li, and X. Liu, Packing edge-colorings of subcubic outerplanar graphs, https://arxiv.org/pdf/2411.05720.pdf.
X. Liu, O. Milenkovic, G. Moustakides, A Combinatorial Proof for the Dowry Problem, 2023 IEEE Information Theory Workshop (ITW).
C. Pan, R. Gabrys, X. Liu, C. Colbourn, O. Milenkovic, Balanced and Swap-Robust Trades for Dynamical Distributed Storage, 2022 IEEE International Symposium on Information Theory (ISIT).
X. Liu and O. Milenkovic, The postdoc problem under the Mallows model, 2021 IEEE International Symposium on Information Theory (ISIT).
A. Kostochka, X. Liu, R. Machado, and O. Milenkovic, Directed intersection representations and the information content of digraphs, 2019 IEEE International Symposium on Information Theory (ISIT).