{"id":7,"date":"2022-01-15T06:00:49","date_gmt":"2022-01-15T06:00:49","guid":{"rendered":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/?page_id=7"},"modified":"2026-04-03T10:48:08","modified_gmt":"2026-04-03T01:48:08","slug":"publications","status":"publish","type":"page","link":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\n

Preprints<\/h2>\n\n\n\n
    \n
  1. Vanishing orders and zero degree Tur\u00e1n densities<\/mark><\/a>, 19 pages.
    with Laihao Ding, Haotian Yang<\/em>
    <\/li>\n\n\n\n
  2. Chromatic thresholds for linear equations and recurrence<\/mark><\/a>, 35 pages.
    with Zhuo Wu, Ningyuan Yang, Shengtong Zhang<\/em>
    <\/li>\n\n\n\n
  3. Colour diversity in spanning structures under Dirac-type conditions<\/mark><\/a>, 14 pages.
    with Xinbu Cheng, Xinqi Huang, Bin Wang, Zhifei Yan<\/em>
    <\/li>\n\n\n\n
  4. Edge-spectral Tur\u00e1n theorems for color-critical graphs with applications<\/mark><\/a>, 26 pages.
    with Yongtao Li, Shengtong Zhang<\/em>
    <\/li>\n\n\n\n
  5. Extremal constructions for apex partite hypergraphs<\/mark><\/a>, 17 pages.
    with Qiyuan Chen, Ke Ye<\/em>
    <\/li>\n\n\n\n
  6. Infinitely many groups exhibiting intermediate growth in maximal sum-free sets<\/mark><\/a>, 19 pages.
    with J\u00f3zsef Balogh<\/em>, Ramon I. Garcia, Ningyuan Yang<\/em>
    <\/li>\n\n\n\n
  7. Multicolor Erd\u0151s–Rogers Functions<\/mark><\/a>, 17 pages.
    with Haoran Luo, Minghui Ouyang<\/em>
    <\/li>\n\n\n\n
  8. An edge-spectral Erd\u0151s-Stone-Simonovits theorem and its stability<\/mark><\/a>, 30 pages.
    with Yongtao Li, Shengtong Zhang<\/em>
    <\/li>\n\n\n\n
  9. Induced rational exponents and bipartite subgraphs in $K_{s,s}$-free graphs<\/mark><\/a>, 21 pages.
    with Zichao Dong, Jun Gao, Ruonan Li<\/em>
    <\/li>\n\n\n\n
  10. On the order of intersecting hypergraphs<\/mark><\/a>, 13 pages.
    with Stijn Cambie, Jaehoon Kim, Hyunwoo Lee, Tuan Tran<\/em>
    <\/li>\n\n\n\n
  11. Interpolating chromatic and homomorphism thresholds<\/mark><\/a>, 29 pages.
    with Xinqi Huang, Mingyuan Rong, Zixiang Xu<\/em>
    <\/li>\n\n\n\n
  12. Induced even cycles in locally sparse graphs<\/mark><\/a>, 13 pages.
    with Laihao Ding, Jun Gao, Bingyu Luan, Shumin Sun<\/em>
    <\/li>\n\n\n\n
  13. Subgraphs of random graphs in hereditary families<\/mark><\/a>, 5 pages.
    with Alexander Clifton, Let\u00edcia Mattos, Michael Zheng<\/em>
    <\/li>\n\n\n\n
  14. Optimal bounds on the polynomial Schur’s theorem<\/mark><\/a>, 24 pages.
    with Jaehoon Kim, P\u00e9ter P\u00e1l Pach<\/em>
    <\/li>\n\n\n\n
  15. Beyond chromatic threshold via $(p,q)$-theorem, and sharp blow-up phenomenon<\/mark><\/a>, 23 pages. An extended abstract of this paper appears in SOCG 2024<\/a>. 
    with Chong Shangguan, Jozef Skokan, Zixiang Xu<\/em>
    <\/li>\n\n\n\n
  16. Graph with any rational density and no rich subsets of linear size<\/mark><\/a>, 10 pages.
    with Seonghyuk Im, Suyun Jiang, Tuan Tran<\/em>
    <\/li>\n\n\n\n
  17. A bandwidth theorem for graph transversals<\/mark><\/a>, 30 pages.
    with Debsoumya Chakraborti, Seonghyuk Im, Jaehoon Kim<\/em>
    <\/li>\n<\/ol>\n\n\n\n

    To appear<\/h2>\n\n\n\n
      \n
    1. More on Nosal\u2019s spectral theorem: Books and 4-cycles<\/mark><\/a>, 23 pages.
      with Yongtao Li, Shengtong Zhang<\/em>
      Journal of Combinatorial Theory, Series B<\/mark><\/li>\n\n\n\n
    2. Stability with minuscule structure for chromatic thresholds<\/mark><\/a>, 26 pages.
      with Jaehoon Kim, Chong Shangguan, Guanghui Wang, Zhuo Wu, Yisai Xue<\/em>
      Peking Mathematical Journal<\/mark><\/li>\n\n\n\n
    3. Set families: restricted distances via restricted intersections<\/mark><\/a>, 17 pages.
      with Zichao Dong, Jun Gao, Minghui Ouyang, Qiang Zhou<\/em>
      Mathematical Proceedings of the Cambridge Philosophical Society<\/mark><\/li>\n\n\n\n
    4. Bipartite Tur\u00e1n problems via graph gluing<\/mark><\/a>, 11 pages.
      with Zichao Dong, Jun Gao<\/em>
      Bulletin of the London Mathematical Society<\/mark><\/li>\n\n\n\n
    5. Isodiametric inequality for vector spaces<\/mark><\/a>, 10 pages.
      with Jiaqi Liao, Guiying Yan<\/em>
      SIAM Journal on Discrete Mathematics<\/mark><\/li>\n\n\n\n
    6. Extremal density for subdivisions with length or sparsity constraints<\/mark><\/a>, 34 pages.
      with Jaehoon Kim, Yantao Tang, Guanghui Wang, Donglei Yang, Fan Yang<\/em>
      Journal of Combinatorial Theory, Series B<\/mark><\/li>\n\n\n\n
    7. Clique density vs blowups<\/mark><\/a>, 22 pages.
      with Domagoj Brada\u010d, Zhuo Wu, Zixiang Xu<\/em>
      Combinatorics, Probability and Computing<\/mark><\/li>\n\n\n\n
    8. Sidorenko’s conjecture for subdivisions and theta substitutions<\/mark><\/a>, 11 pages.
      with Seonghyuk Im, Ruonan Li<\/em>
      Combinatorics, Probability and Computing<\/mark><\/li>\n\n\n\n
    9. Separating hypergraph Tur\u00e1n densities<\/mark><\/a>, 10 pages.
      with Bjarne Sch\u00fclke, Shuaichao Wang, Haotian Yang, Yixiao Zhang<\/em>
      Bulletin of the London Mathematical Society<\/mark><\/li>\n\n\n\n
    10. On $3$-graphs with vanishing codegree Tur\u00e1n density<\/mark><\/a>, 22 pages.
      with Laihao Ding, Ander Lamaison<\/em>, Shuaichao Wang, Haotian Yang<\/em>
      Journal of the London Mathematical Society<\/mark><\/li>\n\n\n\n
    11. Geometric constructions for Ramsey-Tur\u00e1n theory<\/mark><\/a>, 27 pages.
      with Christian Reiher, Maryam Sharifzadeh, Katherine Staden<\/em>
      Journal of the European Mathematical Society<\/mark><\/li>\n\n\n\n
    12. Generalized Ramsey-Tur\u00e1n density for cliques<\/mark><\/a>, 28 pages.
      with Jun Gao, Suyun Jiang, Maya Sankar<\/em>
      Forum of Mathematics, Sigma<\/mark><\/li>\n\n\n\n
    13. New lower bounds on kissing numbers and spherical codes in high dimensions<\/mark><\/a>, 20 pages.
      with Irene Gil Fern\u00e1ndez, Jaehoon Kim, Oleg Pikhurko<\/em>
      American Journal of Mathematics<\/mark><\/li>\n\n\n\n
    14. Extremal number of graphs from geometric shapes<\/mark><\/a>, 23 pages.
      with Jun Gao, Oliver Janzer, Zixiang Xu<\/em>
      Israel Journal of Mathematics<\/mark><\/li>\n<\/ol>\n\n\n\n

      2025<\/h2>\n\n\n\n
        \n
      1. New lower bound on ball packing density in high-dimensional hyperbolic spaces<\/mark><\/a>,
        with Irene Gil Fern\u00e1ndez, Jaehoon Kim, Oleg Pikhurko<\/em>
        International Mathematics Research Notices, Volume 2025, Issue 2, January 2025, rnae282. <\/mark>        https:\/\/doi.org\/10.1093\/imrn\/rnae282<\/a><\/li>\n\n\n\n
      2. Crux, space constraints and subdivisions<\/mark><\/a>,
        with Seonghyuk Im, Jaehoon Kim, Younjin Kim<\/em>
        Journal of Combinatorial Theory, Series B, 170 (2025) 82-127.<\/mark>         https:\/\/doi.org\/10.1016\/j.jctb.2024.08.005<\/a><\/li>\n\n\n\n
      3. Piercing independent sets in graphs without large induced matching<\/mark><\/a>,
        with Jiangdong Ai, Zixiang Xu, Qiang Zhou<\/em>
        Electronic Journal of Combinatorics, 32 (1), (2025), P1-10, 4 pages. <\/mark>        https:\/\/doi.org\/10.37236\/13469<\/a><\/li>\n\n\n\n
      4. Erd\u0151s distinct subset sums problem in a modular setting<\/mark><\/a>,
        with Stijn Cambie, Jun Gao, Younjin Kim<\/em>
        Acta Arithmetica, 217 (2025), 295-307. <\/mark>        https:\/\/doi.org\/10.4064\/aa231107-13-9<\/a><\/li>\n<\/ol>\n\n\n\n

        2024<\/h2>\n\n\n\n
          \n
        1. How connectivity affects the extremal number of trees<\/mark><\/a>,
          with Suyun Jiang, Nika Salia<\/em>
          Journal of Combinatorial Theory, Series B, 167 (2024) 1\u201314.<\/mark> <\/mark>          https:\/\/doi.org\/10.1016\/j.jctb.2024.02.001<\/a><\/li>\n\n\n\n
        2. Rainbow cycles in properly edge-colored graphs<\/mark><\/a>,
          with Jaehoon Kim, Joonkyung Lee, Tuan Tran<\/em>
          Combinatorica, 44, 909\u2013919 (2024).<\/mark>           https:\/\/doi.org\/10.1007\/s00493-024-00101-7<\/a> <\/li>\n\n\n\n
        3. Many Hamiltonian subsets in large graphs with given density<\/mark><\/a>,
          with Stijn Cambie, Jun Gao<\/em>
          Combinatorics, Probability and Computing, 2024; 33(1):110-120.<\/mark>           https:\/\/doi.org\/10.1017\/S0963548323000317<\/a><\/li>\n\n\n\n
        4. On a rainbow extremal problem for color-critical graphs<\/mark><\/a>,
          with Debsoumya Chakraborti, Jaehoon Kim, Hyunwoo Lee, Jaehyeon Seo<\/em>
          Random Structures and Algorithms, 64 (2024), 460\u2013489.           https:\/\/doi.org\/10.1002\/rsa.21189<\/a><\/mark><\/li>\n<\/ol>\n\n\n\n

          2023<\/h2>\n\n\n\n
            \n
          1. A solution to Erd\u0151s and Hajnal\u2019s odd cycle problem<\/mark><\/a>,
            with Richard Montgomery<\/em>
            Journal of the American Mathematical Society, 36 (2023), 1191-1234.             https:\/\/doi.org\/10.1090\/jams\/1018<\/a><\/mark><\/li>\n\n\n\n
          2. Stability from graph symmetrisation arguments with applications to inducibility<\/mark><\/a>,
            with Oleg Pikhurko, Maryam Sharifzadeh, Katherine Staden<\/em>
            Journal of the London Mathematical Society, 108: 1121-1162, 2023.             https:\/\/doi.org\/10.1112\/jlms.12777<\/a><\/mark><\/li>\n\n\n\n
          3. Stability through non-shadows<\/mark><\/a>,
            with Jun Gao, Zixiang Xu<\/em>
            Combinatorica, 43, 1125\u20131137 (2023).<\/mark>             https:\/\/doi.org\/10.1007\/s00493-023-00053-4<\/a><\/mark><\/li>\n\n\n\n
          4. How to build a pillar: a proof of Thomassen\u2019s conjecture<\/mark><\/a>,
            with Irene Gil Fern\u00e1ndez<\/em>
            Journal of Combinatorial Theory, Series B, 162 (2023) 13\u201333.             https:\/\/doi.org\/10.1016\/j.jctb.2023.04.004<\/a><\/mark><\/li>\n\n\n\n
          5. Fractional Helly theorem for Cartesian products of convex sets<\/mark><\/a>,
            with Debsoumya Chakraborti, Jaehoon Kim, Jinha Kim, Minki Kim<\/em>
            Discrete & Computational Geometry, 70, 1632\u20131651, (2023).<\/mark>             https:\/\/doi.org\/10.1007\/s00454-022-00468-8<\/a><\/mark><\/li>\n\n\n\n
          6. Exponential decay of intersection volume with applications on list\u2013decodability and Gilbert\u2013Varshamov type bound<\/mark><\/a>,
            with Jaehoon Kim, Tuan Tran<\/em>
            IEEE Transactions on Information Theory, vol. 69, no. 5, pp. 2841-2854, 2023.<\/mark>             https:\/\/doi.org\/10.1109\/TIT.2022.3232241<\/a><\/li>\n\n\n\n
          7. Disjoint isomorphic balanced clique subdivisions<\/mark><\/a>,
            with Irene Gil Fern\u00e1ndez, Joseph Hyde, Oleg Pikhurko, Zhuo Wu<\/em>
            Journal of Combinatorial Theory, Series B, 161 (2023) 417\u2013436.             https:\/\/doi.org\/10.1016\/j.jctb.2023.03.002<\/a><\/mark><\/li>\n\n\n\n
          8. A proof of Frankl\u2019s conjecture on cross-union families<\/mark><\/a>,
            with Stijn Cambie, Jaehoon Kim, Tuan Tran<\/em>
            Combinatorial Theory, 3 (2), 2023, #9.             https:\/\/doi.org\/10.5070\/C63261987<\/a><\/mark><\/li>\n\n\n\n
          9. Ramsey numbers of cycles versus general graphs<\/mark><\/a>,
            with John Haslegrave, Joseph Hyde, Jaehoon Kim<\/em>
            Forum of Mathematics, Sigma, 11:e10 1\u201318, 2023.<\/mark>             https:\/\/doi.org\/10.1017\/fms.2023.6<\/a><\/li>\n\n\n\n
          10. Shape of the asymptotic maximum sum-free sets in integer lattice grids<\/mark><\/a>,
            with Guanghui Wang, Laurence Wilkies, Donglei Yang<\/em>
            European Journal of Combinatorics, Volume 107, 103614, 2023.<\/mark>             https:\/\/doi.org\/10.1016\/j.ejc.2022.103614<\/a><\/li>\n<\/ol>\n\n\n\n

            2022<\/h2>\n\n\n\n
              \n
            1. Extremal density for sparse minors and subdivisions<\/mark><\/a>,
              with John Haslegrave, Jaehoon Kim<\/em>
              International Mathematics Research Notices, Volume 2022, Issue 20, 15505\u201315548.               https:\/\/doi.org\/10.1093\/imrn\/rnab154<\/a><\/mark><\/li>\n\n\n\n
            2. Nested cycles with no geometric crossings<\/mark><\/a>,
              with Irene Gil Fern\u00e1ndez, Jaehoon Kim, Younjin Kim<\/em>
              Proceedings of the American Mathematical Society, Series B, Volumn 9 (2022), 22-32.               https:\/\/doi.org\/10.1090\/bproc\/107<\/a> <\/mark><\/li>\n\n\n\n
            3. Polynomial Schur’s theorem<\/mark><\/a>,
              with P\u00e9ter P\u00e1l Pach, Csaba S\u00e1ndor<\/em>
              Combinatorica, 42, 1357\u20131384 (2022).               https:\/\/doi.org\/10.1007\/s00493-021-4815-z<\/a><\/mark><\/li>\n\n\n\n
            4. Crux and long cycles in graphs<\/mark><\/a>, <\/em>
              with John Haslegrave, Jie Hu, Jaehoon Kim, Bingyu Luan, Guanghui Wang<\/em>
              SIAM Journal on Discrete Mathematics, Volume 36, Issue 4, 2022.<\/mark>               https:\/\/doi.org\/10.1137\/21M143488X<\/a><\/li>\n\n\n\n
            5. Clique immersion in graphs without fixed bipartite graph<\/mark><\/a>,
              with Guanghui Wang, Donglei Yang<\/em>
              Journal of Combinatorial Theory, Series B, Volume 157, 346-365, 2022. <\/mark>              https:\/\/doi.org\/10.1016\/j.jctb.2022.07.008<\/a><\/li>\n\n\n\n
            6. Well-mixing vertices and almost expanders<\/mark><\/a>,
              with Debsoumya Chakraborti, Jaehoon Kim, Jinha Kim, Minki Kim<\/em>
              Proceedings of the American Mathematical Society, 150, 5097-5110, 2022.               https:\/\/doi.org\/10.1090\/proc\/16090<\/a><\/mark><\/li>\n<\/ol>\n\n\n\n

              2021<\/h2>\n\n\n\n
                \n
              1. The number of maximum primitive sets of integers<\/mark><\/a>,
                with P\u00e9ter P\u00e1l Pach, Rich\u00e1rd Palincza<\/em>
                Combinatorics, Probability and Computing, 30(5), (2021), 781-795. <\/mark><\/li>\n\n\n\n
              2. On the rational Tur\u00e1n exponents conjecture<\/mark><\/a>,
                with Dongyeap Kang, Jaehoon Kim<\/em>
                Journal of Combinatorial Theory, Series B, 148, (2021), 149–172. <\/mark><\/li>\n\n\n\n
              3. Groups with few maximal sum-free sets<\/mark><\/a>,
                with Maryam Sharifzadeh<\/em>
                Journal of Combinatorial Theory, Series A, 177, (2021), 105333, 18 pages. <\/mark><\/li>\n\n\n\n
              4. On the maximum number of integer colourings with forbidden monochromatic sums<\/mark><\/a>,
                with Maryam Sharifzadeh, Katherine Staden<\/em>
                Electronic Journal of Combinatorics, 28 (1), (2021), P1-59, 35 pages. <\/mark><\/li>\n<\/ol>\n\n\n\n

                2020<\/h2>\n\n\n\n
                  \n
                1. The exact minimum number of triangles in graphs of given order and size<\/mark><\/a>,
                  with Oleg Pikhurko, Katherine Staden<\/em>
                  Forum of Mathematics, Pi, 8, E8, (2020), 144 pages. <\/mark><\/li>\n\n\n\n
                2. Asymptotic structure for the clique density theorem<\/mark><\/a>,
                  with Jaehoon Kim, Oleg Pikhurko, Maryam Sharifzadeh<\/em>
                  Discrete Analysis, 2020:19, 26 pp. <\/mark><\/li>\n\n\n\n
                3. Tree decompositions of graphs without large bipartite holes<\/mark><\/a>,
                  with Jaehoon Kim, Younjin Kim<\/em>
                  Random Structures and Algorithms, 57 (1), (2020), 150–168. <\/mark><\/li>\n\n\n\n
                4. Stability and exact Tur\u00e1n numbers for matroids<\/mark><\/a>,
                  with Sammy Luo, Peter Nelson, Kazuhiro Nomoto<\/em>
                  Journal of Combinatorial Theory, Series B, 143, (2020), 29–41. <\/mark><\/li>\n<\/ol>\n\n\n\n

                  2019<\/h2>\n\n\n\n
                    \n
                  1. The number of multiplicative Sidon sets of integers<\/mark><\/a>,
                    with P\u00e9ter P\u00e1l Pach<\/em>
                    Journal of Combinatorial Theory, Series A, 165, (2019), 152–175. <\/mark><\/li>\n\n\n\n
                  2. Edges not in any monochromatic copy of a fixed graph<\/mark><\/a>,
                    with Oleg Pikhurko, Maryam Sharifzadeh<\/em>
                    Journal of Combinatorial Theory, Series B, 135, (2019), 16–43. <\/mark><\/li>\n\n\n\n
                  3. Bivariate fluctuations for the number of arithmetic progressions in random sets<\/mark><\/a>,
                    with Yacine Barhoumi-Andr\u00e9ani, Christoph Koch<\/em>
                    Electronic Journal of Probability, 24 (2019), paper 145, 32 pp. <\/mark><\/li>\n\n\n\n
                  4. Two conjectures in Ramsey-Tur\u00e1n theory<\/mark><\/a>,
                    with Jaehoon Kim, Younjin Kim<\/em>
                    SIAM Journal on Discrete Mathematics, 33 (1), (2019), 564–586. <\/mark><\/li>\n\n\n\n
                  5. A degree sequence Koml\u00f3s theorem<\/mark><\/a>,
                    with Joseph Hyde, Andrew Treglown<\/em>
                    SIAM Journal on Discrete Mathematics, 33 (4), (2019), 2041–2061. <\/mark><\/li>\n\n\n\n
                  6. Structure and supersaturation for intersecting families<\/mark><\/a>,
                    with J\u00f3zsef Balogh, Shagnik Das, Maryam Sharifzadeh, Tuan Tran<\/em>
                    Electronic Journal of Combinatorics, 26 (2), (2019), P2.34, 38 pages. <\/mark><\/li>\n<\/ol>\n\n\n\n

                    2018<\/h2>\n\n\n\n
                      \n
                    1. Sharp bound on the number of maximal sum-free subsets of integers<\/mark><\/a>,
                      with J\u00f3zsef Balogh, Maryam Sharifzadeh, Andrew Treglown<\/em>
                      Journal of the European Mathematical Society, 20 (8), (2018), 1885–1911. <\/mark><\/li>\n\n\n\n
                    2. Rainbow spanning trees in properly coloured complete graphs<\/mark><\/a>,
                      with J\u00f3zsef Balogh, Richard Montgomery<\/em>
                      Discrete Applied Mathematics, 247, (2018), 97–101. <\/mark><\/li>\n<\/ol>\n\n\n\n

                      2017<\/h2>\n\n\n\n
                        \n
                      1. Proof of Koml\u00f3s’s conjecture on Hamiltonian subsets<\/mark><\/a>,
                        with Jaehoon Kim, Maryam Sharifzadeh, Katherine Staden<\/em>
                        Proceedings of the London Mathematical Society, 115 (5), (2017), 974–1013. <\/mark><\/li>\n\n\n\n
                      2. A proof of Mader\u2019s conjecture on large clique subdivisions in C_4-free graphs<\/mark><\/a>,
                        with Richard Montgomery<\/em>
                        Journal of the London Mathematical Society, 95 (1), (2017), 203–222. <\/mark><\/li>\n\n\n\n
                      3. The number of subsets of integers with no k-term arithmetic progression<\/mark><\/a>,
                        with J\u00f3zsef Balogh, Maryam Sharifzadeh<\/em>
                        International Mathematics Research Notices, 20, (2017), 6168–6186. <\/mark><\/li>\n\n\n\n
                      4. Local conditions for exponentially many subdivisions<\/mark><\/a>,
                        with Maryam Sharifzadeh, Katherine Staden<\/em>
                        Combinatorics, Probability and Computing, 26 (3), (2017), 423–430. <\/mark><\/li>\n\n\n\n
                      5. On two problems in Ramsey-Tur\u00e1n theory<\/mark><\/a>,
                        with J\u00f3zsef Balogh, Maryam Sharifzadeh<\/em>
                        SIAM Journal on Discrete Mathematics, 31 (3), (2017), 1848–1866. <\/mark><\/li>\n\n\n\n
                      6. The typical structure of graphs with no large cliques<\/mark><\/a>,
                        with J\u00f3zsef Balogh, Neal Bushaw, Maur\u00edcio Collares Neto, Robert Morris, Maryam Sharifzadeh<\/em>
                        Combinatorica, 37 (4), (2017), 617–632. <\/mark><\/li>\n\n\n\n
                      7. Densities in large permutations and parameter testing<\/mark><\/a>,
                        with Roman Glebov, Carlos Hoppen, Tereza Klimo\u0161ov\u00e1, Yoshiharu Kohayakawa, Daniel Kr\u00e1\u013e<\/em>
                        European Journal of Combinatorics, 60, (2017), 89\u2013-99. <\/mark><\/li>\n<\/ol>\n\n\n\n

                        -2015<\/h2>\n\n\n\n
                          \n
                        1. The number of maximal sum-free subsets of integers<\/mark><\/a>,
                          with J\u00f3zsef Balogh, Maryam Sharifzadeh, Andrew Treglown<\/mark><\/em>
                          Proceedings of the American Mathematical Society, 143, (2015), 4713–4721. <\/mark><\/li>\n\n\n\n
                        2. The typical structure of maximal triangle-free graphs<\/mark><\/a>,
                          with J\u00f3zsef Balogh, \u0160\u00e1rka Pet\u0159\u00ed\u010dkov\u00e1, Maryam Sharifzadeh<\/em>
                          Forum of Mathematics, Sigma, 3, (2015), 19 pages. <\/mark><\/li>\n\n\n\n
                        3. Subdivisions of a large clique in C_6-free graphs<\/mark><\/a>,
                          with J\u00f3zsef Balogh, Maryam Sharifzadeh<\/em>
                          Journal of Combinatorial Theory, Series B, 112, (2015), 18–35. <\/mark><\/li>\n\n\n\n
                        4. Intersecting families of discrete structures are typically trivial<\/mark><\/a>,
                          with J\u00f3zsef Balogh, Shagnik Das, Michelle Delcourt, Maryam Sharifzadeh<\/em>
                          Journal of Combinatorial Theory, Series A, 132, (2015), 224–245. <\/mark><\/li>\n\n\n\n
                        5. On the number of K_4-saturating edges<\/mark><\/a>,
                          with J\u00f3zsef Balogh<\/em>
                          Journal of Combinatorial Theory, Series B, 109, (2014), 250–257.<\/mark><\/li>\n\n\n\n
                        6. Multicolor Ramsey numbers for triple systems<\/mark><\/a>,
                          with Maria Axenovich, Andr\u00e1s Gy\u00e1rf\u00e1s, Dhruv Mubayi<\/em>
                          Discrete Mathematics, 322, (2014) 69\u2013-77.<\/mark><\/li>\n\n\n\n
                        7. Upper bounds on the size of 4- and 6-cycle-free subgraphs of the hypercube<\/mark><\/a>,
                          with J\u00f3zsef Balogh, Ping Hu, Bernard Lidick\u00fd<\/em>
                          European Journal of Combinatorics, 35, (2014), 75–85.<\/mark><\/li>\n\n\n\n
                        8. On the Turan number of forests<\/mark><\/a>,
                          with Bernard Lidick\u00fd, Cory Palmer<\/em>
                          Electronic Journal of Combinatorics, 20 (2), (2013), paper 62, 14pp.<\/mark><\/li>\n\n\n\n
                        9. The biased odd cycle game<\/mark><\/a>,
                          with Asaf Ferber, Roman Glebov, Michael Krivelevich, Cory Palmer, Tomas Valla, M\u00e1t\u00e9 Vizer<\/em>
                          Electronic Journal of Combinatorics, 20 (2), (2013), paper 9, 10pp.<\/mark><\/li>\n\n\n\n
                        10. Extremal graphs for blow-ups of cycles and trees<\/mark><\/a>,
                          Electronic Journal of Combinatorics, 20 (1), (2013), paper 65, 16pp.<\/mark><\/li>\n\n\n\n
                        11. Dominating sets in triangulations on surfaces<\/mark><\/a>,
                          with Michael Pelsmajer<\/em>
                          Ars Math. Contemp., 4, (2011), 177–204.<\/mark><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

                          Preprints To appear 2025 2024 2023 2022 2021 2020 2019 2018 2017 -2015<\/p>\n","protected":false},"author":5,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7","page","type-page","status-publish","hentry"],"featured_image_src":null,"_links":{"self":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/pages\/7","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/comments?post=7"}],"version-history":[{"count":123,"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/pages\/7\/revisions"}],"predecessor-version":[{"id":530,"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/pages\/7\/revisions\/530"}],"wp:attachment":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/media?parent=7"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}