Publications

Preprints

A proof of Frankl’s conjecture on cross-union families, with S. Cambie, J. Kim, T. Tran, 9 pages. PDF
How to build a pillar: a proof of Thomassen’s conjecture, with I. Gil Fernández, 16 pages. PDF
Exponential decay of intersection volume with applications on list–decodability and Gilbert–Varshamov type bound, with J. Kim, T. Tran, 25 pages. PDF
Ramsey numbers of cycles versus general graphs, with J. Haslegrave, J. Hyde, J. Kim, 20 pages. PDF
New lower bounds on kissing numbers and spherical codes in high dimensions, with I. Gil Fernández, J. Kim, O. Pikhurko, 20 pages. PDF
Well-mixing vertices and almost expanders, with D. Chakraborti, J. Kim, J. Kim, M. Kim, 13 pages. PDF
Fractional Helly theorem for Cartesian products of convex sets, with D. Chakraborti, J. Kim, J. Kim, M. Kim, 16 pages. PDF
Shape of the asymptotic maximum sum-free sets in integer lattice grids, with G. Wang, L. Wilkies, D. Yang, 17 pages. PDF
Crux and long cycles in graphs, with J. Haslegrave, J. Hu, J. Kim, B. Luan, G. Wang, 13 pages. PDF
Geometric constructions for Ramsey-Turán theory, with C. Reiher, M. Sharifzadeh, K. Staden, 27 pages. PDF
Stability from graph symmetrisation arguments with applications to inducibility, with O. Pikhurko, M. Sharifzadeh, K. Staden, 41 pages. PDF
A solution to Erdős and Hajnal’s odd cycle problem, with R. Montgomery, 42 pages. PDF
Clique immersion in graphs without fixed bipartite graph, with G. Wang, D. Yang, 12 pages. PDF

Polynomial Schur's theorem, with P. Pach, Cs. Sándor
Combinatorica, 21 pages. PDF
Nested cycles with no geometric crossings, with I. Gil Fernández, J. Kim, Y. Kim
Proceedings of the American Mathematical Society, 9 pages. PDF
Extremal density for sparse minors and subdivisions, with J. Haslegrave, J. Kim
International Mathematics Research Notices , 44 pages. PDF

The number of maximum primitive sets of integers, with P. Pach, R. Palincza
Combinatorics, Probability and Computing , 30(5), (2021), 781-795. PDF
On the rational Turán exponents conjecture, with D. Kang, J. Kim
Journal of Combinatorial Theory, Series B , 148, (2021), 149--172. PDF
Groups with few maximal sum-free sets, with M. Sharifzadeh
Journal of Combinatorial Theory, Series A, 177, (2021), 105333, 18 pages. PDF
On the maximum number of integer colourings with forbidden monochromatic sums, with M. Sharifzadeh, K. Staden
Electronic Journal of Combinatorics, 28 (1), (2021), P1-59, 35 pages. PDF

The exact minimum number of triangles in graphs of given order and size, with O. Pikhurko, K. Staden
Forum of Mathematics, Pi , 8, E8, (2020), 144 pages. PDF
Asymptotic structure for the clique density theorem, with J. Kim, O. Pikhurko, M. Sharifzadeh
Discrete Analysis , 2020:19, 26 pp. PDF
Tree decompositions of graphs without large bipartite holes, with J. Kim, Y. Kim
Random Structures and Algorithms, 57 (1), (2020), 150--168. PDF
Stability and exact Turán numbers for matroids, with S. Luo, P. Nelson, K. Nomoto
Journal of Combinatorial Theory, Series B, 143, (2020), 29--41. PDF

The number of multiplicative Sidon sets of integers, with P. Pach
Journal of Combinatorial Theory, Series A, 165, (2019), 152--175. PDF
Edges not in any monochromatic copy of a fixed graph, with O. Pikhurko, M. Sharifzadeh
Journal of Combinatorial Theory, Series B, 135, (2019), 16--43. PDF
Bivariate fluctuations for the number of arithmetic progressions in random sets, with Y. Barhoumi-Andréani, C. Koch
Electronic Journal of Probability, 24 (2019), paper 145, 32 pp. PDF
Two conjectures in Ramsey-Turán theory, with J. Kim, Y. Kim
SIAM Journal on Discrete Mathematics, 33 (1), (2019), 564--586. PDF
A degree sequence Komlós theorem, with J. Hyde, A. Treglown
SIAM Journal on Discrete Mathematics, 33 (4), (2019), 2041--2061. PDF
Structure and supersaturation for intersecting families, with J. Balogh, S. Das, M. Sharifzadeh, T. Tran
Electronic Journal of Combinatorics, 26 (2), (2019), P2.34, 38 pages. PDF

Sharp bound on the number of maximal sum-free subsets of integers, with J. Balogh, M. Sharifzadeh, A. Treglown
Journal of the European Mathematical Society, 20 (8), (2018), 1885--1911. PDF
Rainbow spanning trees in properly coloured complete graphs, with J. Balogh, R. Montgomery
Discrete Applied Mathematics, 247, (2018), 97--101. PDF

Proof of Komlós's conjecture on Hamiltonian subsets, with J. Kim, M. Sharifzadeh, K. Staden
Proceedings of the London Mathematical Society, 115 (5), (2017), 974--1013. PDF
A proof of Mader’s conjecture on large clique subdivisions in C_4-free graphs, with R. Montgomery
Journal of the London Mathematical Society, 95 (1), (2017), 203--222. PDF
The number of subsets of integers with no k-term arithmetic progression, with J. Balogh, M. Sharifzadeh
International Mathematics Research Notices, 20, (2017), 6168--6186. PDF
Local conditions for exponentially many subdivisions, with M. Sharifzadeh, K. Staden
Combinatorics, Probability and Computing, 26 (3), (2017), 423--430. PDF
On two problems in Ramsey-Turán theory, with J. Balogh, M. Sharifzadeh
SIAM Journal on Discrete Mathematics, 31 (3), (2017), 1848--1866. PDF
The typical structure of graphs with no large cliques, with J. Balogh, N. Bushaw, M. Collares Neto, R. Morris, M. Sharifzadeh
Combinatorica, 37 (4), (2017), 617--632. PDF
Densities in large permutations and parameter testing, with R. Glebov, C. Hoppen, T. Klimošová, Y. Kohayakawa, D. Kráľ
European Journal of Combinatorics, 60, (2017), 89–-99. PDF

The number of maximal sum-free subsets of integers, with J. Balogh, M. Sharifzadeh, A. Treglown
Proceedings of the American Mathematical Society, 143, (2015), 4713--4721. PDF
The typical structure of maximal triangle-free graphs, with J. Balogh, S. Petříčková, M. Sharifzadeh
Forum of Mathematics, Sigma, 3, (2015), 19 pages. PDF
Subdivisions of a large clique in C_6-free graphs, with J. Balogh, M. Sharifzadeh
Journal of Combinatorial Theory, Series B, 112, (2015), 18--35. PDF
Intersecting families of discrete structures are typically trivial, with J. Balogh, S. Das, M. Delcourt, M. Sharifzadeh
Journal of Combinatorial Theory, Series A, 132, (2015), 224--245. PDF

On the number of K_4-saturating edges, with J. Balogh
Journal of Combinatorial Theory, Series B, 109, (2014), 250--257. PDF
Multicolor Ramsey numbers for triple systems, with M. Axenovich, A. Gyárfás, D. Mubayi
Discrete Mathematics, 322, (2014) 69–-77. PDF
Upper bounds on the size of 4- and 6-cycle-free subgraphs of the hypercube, with J. Balogh, P. Hu, B. Lidický
European Journal of Combinatorics, 35, (2014), 75--85. PDF

On the Turan number of forests, with B. Lidický, C. Palmer
Electronic Journal of Combinatorics, 20 (2), (2013), paper 62, 14pp. PDF
The biased odd cycle game, with A. Ferber, R. Glebov, M. Krivelevich, C. Palmer, T. Valla, M. Vizer
Electronic Journal of Combinatorics, 20 (2), (2013), paper 9, 10pp. PDF
Extremal graphs for blow-ups of cycles and trees
Electronic Journal of Combinatorics, 20 (1), (2013), paper 65, 16pp. PDF
Dominating sets in triangulations on surfaces, with M. Pelsmajer
Ars Math. Contemp., 4, (2011), 177--204. PDF