Papers and preprints

Preprints

• Building graphs with high minimum degree on a budget (with Kyriakos Katsamaktsis), submitted.
• Thresholds for constrained Ramsey and anti-Ramsey problems (with Natalie Behague, Joseph Hyde, Robert Hancock, Natasha Morrison), submitted.
• Rainbow subgraphs of uniformly coloured randomly perturbed graphs (with Kyriakos Katsamaktsis and Amedeo Sgueglia), submitted.
• Ascending subgraph decomposition (with Kyriakos Katsamaktsis, Alexey Pokrovskiy, and Benny Sudakov), submitted.
  See here for slides.
• Pancyclicity of highly connected graphs, submitted.
• Decomposing cubic graphs into isomorphic linear forests (with Gal Kronenberg, Alexey Pokrovskiy, and Liana Yepremyan), submitted.
• Chi-boundedness of graphs containing no cycles with \(k\) chords (with Joonkyung Lee and Alexey Pokrovskiy), submitted.
  See here for slides.
• Size-Ramsey numbers of powers of hypergraph trees and long subdivisions (with Alexey Pokrovskiy and Liana Yepremyan), submitted.
  See here for slides.
• Fractional triangle decompositions in almost complete graphs (with Vytautas Gruslys), manuscript.
  See link for the certificates given by the computer search used in this paper.
  See here for slides.
• Monochromatic triangle packings in red-blue graphs (with Vytautas Gruslys), manuscript.
  See link for the certificates given by the computer search used in this paper.
  See here for slides.
• Almost partitioning the hypercube into copies of a graph (with Vytautas Gruslys), manuscript.

To appear

• Partitioning a tournament into sub-tournaments of high connectivity (with António Girão), Combinatorica, to appear.
• On a problem of Brown, Erdős and Sós (with Amedeo Sgueglia), Proc. Am. Math. Soc., to appear.

2024

• Directed cycles with zero weight in \(\mathbb{Z}^k_p\) (with Natasha Morrison), J. Combin. Theory Ser. B. 168 (2024), 192–207.
  See here for slides.
• Separating paths systems of almost linear size, Trans. Amer. Math. Soc. 377 (2024) 5583–5615.
• Sublinear expanders and their applications, In Surveys in Combinatorics 2024 (F. Fischer and R. Johnson, Eds.) London Mathematical Society Lecture Note Series, 2024, pp. 89–130.
  See here for slides.
• Rainbow Hamiltonicity in uniformly coloured perturbed digraphs (with Kyriakos Katsamaktsis and Amedeo Sgueglia), Combin. Probab. Comput. 33 (2024) 624–642.
  See here for an undirected version.
• The rainbow saturation number is linear (with Natalie Behague, Tom Johnston, Shannon Ogden, and Natasha Morrison), SIAM J. Disc. Math 38 (2024), 1239–1249.
• The Turán density of tight cycles in three-uniform hypergraphs (with Alexey Pokrovskiy and Nina Kamčev), Int. Math. Res. Not. (IMRN) 2024 (2023), 4804–4841.
  See here for slides.
• Rainbow subdivisions of cliques (with Tao Jiang, Abhishek Methuku, and Liana Yepremyan), Random Struct. Algo. 64 (2024), 625–644.

2023

• Immersion of complete digraphs in Eulerian digraphs (with António Girão), Israel J. Math. 260 (2023), 401–425.
  See here for a translation of a vaguely related paper of Mader from German.
  See here for slides.
• Hypergraphs with no tight cycles, Proc. Am. Math. Soc. 151 (2023), 455–462.
  See here for slides.

2022

• Large rainbow cliques in randomly perturbed dense graphs (with Elad Aigner-Horev, Oran Danon, and Danny Hefetz), SIAM J. Disc. Math. 36 (2022), 2975–2994.
• Optimal adaptive detection of monotone patterns (with Omri Ben-Eliezer and Erik Waingarten), ICALP (2022), 17:1–17:19.
  See here for the arxiv version.
  See here for slides.
• An improvement on Łuczak's connected matchings method, Bull. London. Math. Soc. 54 (2022), 609–623.
  See here for slides.
• Small rainbow cliques in randomly perturbed dense graphs (with Elad Aigner-Horev, Oran Danon, and Danny Hefetz), Europ. J. Combin. 101 (2022), 103452.

2021

• The size-Ramsey number of 3-uniform tight paths (with Jie Han, Yoshiharu Kohayakawa, Guilherme Oliveira Mota, and Olaf Parczyk), Adv. Combin. (2021).
• Cycle partitions of regular graphs (with Vytautas Gruslys), Combin. Probab. Comput. 30 (2021), 526–549.
  See here for an older version with an extended proof of Lemma 4.
  See here for slides.
• Hypergraph Lagrangians II: when colex is best (with Vytautas Gruslys and Natasha Morrison), Israel J. Math. 242 (2021), 637–662.
  See here for slides.
• Minimum degree conditions for monochromatic cycle partitioning (with Dániel Korándi, Richard Lang, and Alexey Pokrovskiy), J. Combin. Theory Ser. B 146 (2021), 96–123.

2020

• Orthonormal representations of H-free graphs (with Igor Balla and Benny Sudakov), Discrete Comput. Geom. 64 (2020), 654–670.
• The oriented size Ramsey number of directed paths (with Benny Sudakov), European J. Combin. 88 (2020), 103103.
• Monochromatic trees in random tournaments (with Matija Bucić, Sven Heberle, and Benny Sudakov), Combin. Probab. Comput. 29 (2020), 318–345.
• On Existentially Complete Triangle-free Graphs (with Julian Sahasrabudhe), Israel J. Math. 236 (2020), 591–601.
• Dense induced bipartite subgraphs in triangle-free graphs (with Matthew Kwan, Benny Sudakov and Tuan Tran), Combinatorica 40 (2020), 283–305.
  See here for slides.
• Hypergraph Lagrangians I: the Frankl-Füredi conjecture is false (with Vytautas Gruslys and Natasha Morrison), Adv. Math. 365 (2020), 107063.
  See here for slides.
• Product-free sets in the free semigroup (with Imre Leader, Bhargav Narayanan, and Mark Walters), European J. Combin. 83 (2020), 103003.
• Many H-copies in graphs with a forbidden tree, SIAM J. Discrete Math. 33 (2020), 2360–2368.

2019

• Finding monotone patterns in sublinear time (with Omri Ben-Eliezer, Clément L. Canonne, and Erik Waingarten), FOCS 2019.
  See here for slides.
• Multicolour bipartite Ramsey number of paths (with Matija Bucić and Benny Sudakov), Electron. J. Combin. 26 (2019), P3.60.
• 3-colour bipartite Ramsey number of cycles and paths (with Matija Bucić and Benny Sudakov), J. Graph Theory 92 (2019), 445–459.
• Partitioning a graph into monochromatic connected subgraphs (with António Girão and Julian Sahasrabudhe), J. Graph Theory 91 (2019), 353–364.
• Directed Ramsey number for trees (with Matija Bucić and Benny Sudakov), J. Combin. Theory Ser. B 137 (2019), 145–177.
  here for slides.
• Monochromatic cycle partitions of 2-coloured graphs with minimum degree 3n/4, Electron. J. Combin. 26 (2019), P1.19.
  See here for slides.
• The homomorphism threshold of {C_3,C_5}-free graphs (with Richard Snyder), J. Graph Theory 90 (2019), 83–106.
• Monochromatic paths in random tournament (with Matija Bucić and Benny Sudakov), Random Struct. Algo. 54 (2019), 69–81.
  See here for slides.

2018

• Minimum saturated families of sets (with Matija Bucić, Benny Sudakov, and Tuan Tran), Bull. London Math. Soc. 50 (2018), 725–732.
• Minimizing the number of triangular edges (with Vytautas Gruslys), Combin. Probab. Comput. 27 (2018), 580–622.
• Eigenvalues of subgraphs of the cube (with Béla Bollobás and Jonathan Lee), European J. Combin. 70 (2018), 125–148.
• Longest common extension (with Béla Bollobás), European J. Combin. 68 (2018), 242–248.

2012–2017

• Radon numbers for trees, Discr. Math. 340 (2017), 333–344.
• Path Ramsey number for random graphs, Combin. Probab. Comput. 25 (2016), 612–622.
• Large monochromatic triple stars in edge colourings, J. Graph Theory 80 (2015), 323–328.
• Separating path systems (with Victor Falgas-Ravry, Teeradej Kittipassorn, Dániel Korándi, and Bhargav Narayanan), J. Combin. 5 (2014), 335–354.
• The property of having a k-regular subgraph has a sharp threshold, Random Struct. Algo. 42 (2012), 509–519.