**Preprints**

- Crux, space constraints and subdivisions, 37 pages.
*with Seonghyuk Im, Jaehoon Kim, Younjin Kim* - Disjoint isomorphic balanced clique subdivisions, 17 pages.
*with Irene Gil Fernández, Joseph Hyde, Oleg Pikhurko, Zhuo Wu* - On a rainbow extremal problem for color-critical graphs, 28 pages.

with*Debsoumya Chakraborti, Jaehoon Kim, Hyunwoo Lee, Jaehyeon Seo* - A proof of Frankl’s conjecture on cross-union families, 9 pages.
*with Stijn Cambie, Jaehoon Kim, Tuan Tran* - How to build a pillar: a proof of Thomassen’s conjecture, 16 pages.
*with Irene Gil Fernández* - Exponential decay of intersection volume with applications on list–decodability and Gilbert–Varshamov type bound, 25 pages.
*with Jaehoon Kim, Tuan Tran* - Ramsey numbers of cycles versus general graphs, 20 pages.
*with John Haslegrave, Joseph Hyde, Jaehoon Kim* - New lower bounds on kissing numbers and spherical codes in high dimensions, 20 pages.
*with Irene Gil Fernández, Jaehoon Kim, Oleg Pikhurko* - Shape of the asymptotic maximum sum-free sets in integer lattice grids, 17 pages.
*with Guanghui Wang, Laurence Wilkies, Donglei Yang* - Crux and long cycles in graphs, 13 pages.
*with John Haslegrave, Jie Hu, Jaehoon Kim, Bingyu Luan, Guanghui Wang* - Geometric constructions for Ramsey-Turán theory, 27 pages.
*with Christian Reiher, Maryam Sharifzadeh, Katherine Staden* - Stability from graph symmetrisation arguments with applications to inducibility, 41 pages.
*with Oleg Pikhurko, Maryam Sharifzadeh, Katherine Staden* - Clique immersion in graphs without fixed bipartite graph, 12 pages.
*with Guanghui Wang, Donglei Yang*

**To appear**

- A solution to Erdős and Hajnal’s odd cycle problem, 42 pages.
*with Richard Montgomery*

Journal of the American Mathematical Society - Well-mixing vertices and almost expanders, 13 pages
*with Debsoumya Chakraborti, Jaehoon Kim, Jinha Kim, Minki Kim*

Proceedings of the American Mathematical Society - Fractional Helly theorem for Cartesian products of convex sets, 16 pages
*with Debsoumya Chakraborti, Jaehoon Kim, Jinha Kim, Minki Kim*

Discrete & Computational Geometry - Polynomial Schur’s theorem, 21 pages
*with Péter Pál Pach, Csaba Sándor*

Combinatorica - Nested cycles with no geometric crossings, 9 pages
*with Irene Gil Fernández, Jaehoon Kim, Younjin Kim*

Proceedings of the American Mathematical Society - Extremal density for sparse minors and subdivisions, 44 pages
*with John Haslegrave, Jaehoon Kim*

International Mathematics Research Notices

**2021**

- The number of maximum primitive sets of integers,
*with Péter Pál Pach, Richárd Palincza*

Combinatorics, Probability and Computing, 30(5), (2021), 781-795. - On the rational Turán exponents conjecture,
*with Dongyeap Kang, Jaehoon Kim*

Journal of Combinatorial Theory, Series B, 148, (2021), 149–172. - Groups with few maximal sum-free sets,
*with Maryam Sharifzadeh*

Journal of Combinatorial Theory, Series A, 177, (2021), 105333, 18 pages. - On the maximum number of integer colourings with forbidden monochromatic sums,
*with Maryam Sharifzadeh, Katherine Staden*

Electronic Journal of Combinatorics, 28 (1), (2021), P1-59, 35 pages.

**2020**

- The exact minimum number of triangles in graphs of given order and size,
*with Oleg Pikhurko, Katherine Staden*

Forum of Mathematics, Pi, 8, E8, (2020), 144 pages. - Asymptotic structure for the clique density theorem,
*with Jaehoon Kim, Oleg Pikhurko, Maryam Sharifzadeh*

Discrete Analysis, 2020:19, 26 pp. - Tree decompositions of graphs without large bipartite holes,
*with Jaehoon Kim, Younjin Kim*

Random Structures and Algorithms, 57 (1), (2020), 150–168. - Stability and exact Turán numbers for matroids,
*with Sammy Luo, Peter Nelson, Kazuhiro Nomoto*

Journal of Combinatorial Theory, Series B, 143, (2020), 29–41.

**2019**

- The number of multiplicative Sidon sets of integers,
*with Péter Pál Pach*

Journal of Combinatorial Theory, Series A, 165, (2019), 152–175. - Edges not in any monochromatic copy of a fixed graph,
*with Oleg Pikhurko, Maryam Sharifzadeh*

Journal of Combinatorial Theory, Series B, 135, (2019), 16–43. - Bivariate fluctuations for the number of arithmetic progressions in random sets,
*with Yacine Barhoumi-Andréani, Christoph Koch*

Electronic Journal of Probability, 24 (2019), paper 145, 32 pp. - Two conjectures in Ramsey-Turán theory,
*with Jaehoon Kim, Younjin Kim*

SIAM Journal on Discrete Mathematics, 33 (1), (2019), 564–586. - A degree sequence Komlós theorem,
*with Joseph Hyde, Andrew Treglown*

SIAM Journal on Discrete Mathematics, 33 (4), (2019), 2041–2061. - Structure and supersaturation for intersecting families,
*with József Balogh, Shagnik Das, Maryam Sharifzadeh, Tuan Tran*

Electronic Journal of Combinatorics, 26 (2), (2019), P2.34, 38 pages.

**2018**

- Sharp bound on the number of maximal sum-free subsets of integers,
*with József Balogh, Maryam Sharifzadeh, Andrew Treglown*

Journal of the European Mathematical Society, 20 (8), (2018), 1885–1911. - Rainbow spanning trees in properly coloured complete graphs,
*with József Balogh, Richard Montgomery*

Discrete Applied Mathematics, 247, (2018), 97–101.

**2017**

- Proof of Komlós’s conjecture on Hamiltonian subsets,
*with Jaehoon Kim, Maryam Sharifzadeh, Katherine Staden*

Proceedings of the London Mathematical Society, 115 (5), (2017), 974–1013. - A proof of Mader’s conjecture on large clique subdivisions in C_4-free graphs,
*with Richard Montgomery*

Journal of the London Mathematical Society, 95 (1), (2017), 203–222. - The number of subsets of integers with no k-term arithmetic progression,
*with József Balogh, Maryam Sharifzadeh*

International Mathematics Research Notices, 20, (2017), 6168–6186. - Local conditions for exponentially many subdivisions,
*with Maryam Sharifzadeh, Katherine Staden*

Combinatorics, Probability and Computing, 26 (3), (2017), 423–430. - On two problems in Ramsey-Turán theory,
*with József Balogh, Maryam Sharifzadeh*

SIAM Journal on Discrete Mathematics, 31 (3), (2017), 1848–1866. - The typical structure of graphs with no large cliques,
*with József Balogh, Neal Bushaw, Maurício Collares Neto, Robert Morris, Maryam Sharifzadeh*

Combinatorica, 37 (4), (2017), 617–632. - Densities in large permutations and parameter testing,
*with Roman Glebov, Carlos Hoppen, Tereza Klimošová, Yoshiharu Kohayakawa, Daniel Kráľ*

European Journal of Combinatorics, 60, (2017), 89–-99.

## –**2015**

- The number of maximal sum-free subsets of integers,
*with József Balogh, Maryam Sharifzadeh, Andrew Treglown*

Proceedings of the American Mathematical Society, 143, (2015), 4713–4721. - The typical structure of maximal triangle-free graphs,
*with József Balogh, Šárka Petříčková, Maryam Sharifzadeh*

Forum of Mathematics, Sigma, 3, (2015), 19 pages. - Subdivisions of a large clique in C_6-free graphs,
*with József Balogh, Maryam Sharifzadeh*

Journal of Combinatorial Theory, Series B, 112, (2015), 18–35. - Intersecting families of discrete structures are typically trivial,
*with József Balogh, Shagnik Das, Michelle Delcourt, Maryam Sharifzadeh*

Journal of Combinatorial Theory, Series A, 132, (2015), 224–245. - On the number of K_4-saturating edges,
*with József Balogh*

Journal of Combinatorial Theory, Series B, 109, (2014), 250–257. - Multicolor Ramsey numbers for triple systems,
*with Maria Axenovich, András Gyárfás, Dhruv Mubayi*

Discrete Mathematics, 322, (2014) 69–-77. - Upper bounds on the size of 4- and 6-cycle-free subgraphs of the hypercube,
*with József Balogh, Ping Hu, Bernard Lidický*

European Journal of Combinatorics, 35, (2014), 75–85. - On the Turan number of forests,
*with Bernard Lidický, Cory Palmer*

Electronic Journal of Combinatorics, 20 (2), (2013), paper 62, 14pp. - The biased odd cycle game,
*with Asaf Ferber, Roman Glebov, Michael Krivelevich, Cory Palmer, Tomas Valla, Máté Vizer*

Electronic Journal of Combinatorics, 20 (2), (2013), paper 9, 10pp. - Extremal graphs for blow-ups of cycles and trees,

Electronic Journal of Combinatorics, 20 (1), (2013), paper 65, 16pp. - Dominating sets in triangulations on surfaces,
*with Michael Pelsmajer*

Ars Math. Contemp., 4, (2011), 177–204.