Research

I am interested in combinatorics and graph theory, specifically coloring of graphs, Ramsey theory and probabilistic combinatorics.

Publications and Preprints

Journal Publications and Preprints:

  1. J. Balogh, A. Kostochka, and X. Liu, Packing chromatic number of cubic graphs, Discrete Math. 341 (2018), 474--483. (slides: 20 mins and 50 mins)
  2. 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)
  3. 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)
  4. J. Geneson, A. Holmes, X. Liu, D. Neidinger, Y. Pehova, and I. Wass, Ramsey numbers of ordered graphs under graph operations, Submitted.
  5. X. Liu, R. Machado, and O. Milenkovic, Directed intersection representations and the information content of digraphs , Submitted. (Slides)
  6. J. Balogh, A. Kostochka, M. Lavrov, and X. Liu, Monochromatic connected matchings in 2-edge-colored multipartite graphs, Submitted.
  7. J. Balogh, A. Kostochka, M. Lavrov, and X. Liu, Long monochromatic paths and cycles in 2-edge-colored multipartite graphs, Submitted. (slides: 20 mins and 50 mins)
  8. J. Balogh, A. Kostochka, M. Lavrov, and X. Liu, Long monochromatic paths and cycles in 2-edge-colored graphs with large minimum degree, Submitted. (slides: 20 mins)
  9. J. Balogh, A. Kostochka, M. Lavrov, and X. Liu, Monochromatic cycles of given length in 2-edge-colored graphs with large minimum degree, In Preparation.
  10. R. Liu, X. Liu, M. Rolek, and G. Yu, Packing (1,1,2,2)-coloring of some subcubic graphs, Submitted.

Conference Publication:

  1. 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).