Andrew Treglown Preprints and publications

• Surveys in Combinatorics 2019 (joint editor with Allan Lo, Richard Mycroft and Guillem Perarnau)

• Tilings in vertex ordered graphs (with József Balogh and Lina Li)
• An asymmetric random Rado theorem for single equations: the 0-statement (with Robert Hancock)
• Transitive tournament tilings in oriented graphs with large minimum total degree (with Allan Lo, Louis DeBiasio and Theo Molla)

• Vertex Ramsey properties of randomly perturbed graphs (with Shagnik Das and Patrick Morris, Random Structures and Algorithms, to appear)
• A discrepancy version of the Hajnal-Szemerédi theorem (with József Balogh, Béla Csaba and András Pluhár, Combinatorics, Probability and Computing, to appear)
• Tilings in randomly perturbed graphs: bridging the gap between Hajnal-Szemerédi and Johansson-Kahn-Vu (with Jie Han and Patrick Morris, Random Structures and Algorithms, to appear)
• Existence thresholds and Ramsey properties of random posets (with Victor Falgas-Ravry, Klas Markström and Yi Zhao, Random Structures and Algorithms, to appear)
• The bandwidth theorem for locally dense graphs (with Katherine Staden, Forum of Mathematics, Sigma, to appear)
• Ramsey properties of randomly perturbed graphs: cliques and cycles (with Shagnik Das, Combinatorics, Probability and Computing, to appear)

• A degree sequence version of the Kühn-Osthus tiling theorem (with Joseph Hyde, Electronic Journal of Combinatorics 27(3) (2020) #P3.48, 30 pages)
• The complexity of perfect matchings and packings in dense hypergraphs (with Jie Han, J. Combinatorial Theory Series B 141 (2020) 72-104)

• A degree sequence Komlós theorem (with Joseph Hyde and Hong Liu, SIAM Journal on Discrete Mathematics 33 (2019) 2041-2061)
• Tilings in randomly perturbed dense graphs (with József Balogh and Adam Zsolt Wagner, Combinatorics, Probability and Computing 28 (2019) 159-176)
• Independent sets in hypergraphs and Ramsey properties of graphs and the integers (with Robert Hancock and Katherine Staden, SIAM Journal on Discrete Mathematics 33 (2019) 153-188)

• Sharp bound on the number of maximal sum-free subsets of integers (with József Balogh, Hong Liu and Maryam Sharifzadeh, Journal of the European Mathematical Society 20 (2018) 1885-1911)
• On the complexity of finding and counting solution-free sets of integers (with Kitty Meeks, Discrete Applied Mathematics 243 (2018) 219-238)
• Tiling directed graphs with tournaments (with Andrzej Czygrinow, Louis DeBiasio and Theo Molla, Forum of Mathematics, Sigma 6 (2018) e2, 53 pages)

• Exact minimum codegree threshold for K^-_4-factors (with Jie Han, Allan Lo and Yi Zhao, Combinatorics, Probability and Computing 26 (2017) 856-885)
• On solution-free sets of integers II (with Robert Hancock, Acta Arithmetica 180 (2017) 15-33)
• On solution-free sets of integers (with Robert Hancock, European Journal of Combinatorics 66 (2017) 110-128)
• An improved lower bound for Folkman's Theorem (with József Balogh, Sean Eberhard, Bhargav Narayanan and Adam Zsolt Wagner, Bulletin of the London Mathematical Society 49 (2017) 745-747)
• On degree sequences forcing the square of a Hamilton cycle (with Katherine Staden, SIAM Journal on Discrete Mathematics 31 (2017) 383-437)

• Applications of graph containers in the Boolean lattice (with József Balogh and Adam Zsolt Wagner, Random Structures and Algorithms 49 (2016) 845-872)
• Proof of the 1-factorization and Hamilton decomposition conjectures (with Béla Csaba, Daniela Kühn, Allan Lo and Deryk Osthus, Memoirs of the American Mathematical Society 244 (2016), monograph 1154, 170 pages)
• A degree sequence Hajnal-Szemerédi theorem (J. Combinatorial Theory Series B 118 (2016) 13-43)
• A note on perfect matchings in uniform hypergraphs (with Yi Zhao, Electronic Journal of Combinatorics 23(1) (2016) #P1.16, 14 pages)

• On directed versions of the Hajnal-Szemerédi theorem (Combinatorics, Probability and Computing 24 (2015) 873-928)
• The number of maximal sum-free subsets of integers (with József Balogh, Hong Liu and Maryam Sharifzadeh, Proceedings of the American Mathematical Society, 143 (2015) 4713-4721)

• A random version of Sperner's theorem (with József Balogh and Richard Mycroft, J. Combinatorial Theory Series A, 128 (2014) 104-110)

• Monochromatic triangles in three-coloured graphs (with James Cummings, Daniel Král', Florian Pfender, Konrad Sperfeld and Michael Young, J. Combinatorial Theory Series B 103 (2013) 489-503)
• Exact minimum degree thresholds for perfect matchings in uniform hypergraphs II (with Yi Zhao, J. Combinatorial Theory Series A 120 (2013) 1463-1482)
• On perfect packings in dense graphs (with József Balogh and Alexandr V. Kostochka, Electronic Journal of Combinatorics 20(1) (2013) #P57, 17 pages)
• Matchings in 3-uniform hypergraphs (with Daniela Kühn and Deryk Osthus, J. Combinatorial Theory Series B 103 (2013) 291-305)
• Embedding spanning bipartite graphs of small bandwidth (with Fiachra Knox, Combinatorics, Probability and Computing 22 (2013) 71-96)

• Exact minimum degree thresholds for perfect matchings in uniform hypergraphs (with Yi Zhao, J. Combinatorial Theory Series A 119 (2012) 1500-1522)
• A note on some embedding problems for oriented graphs (Journal of Graph Theory 69 (2012) 330-336)

• Hamilton decompositions of regular tournaments (with Daniela Kühn and Deryk Osthus, Proceedings of the London Mathematical Society 101 (2010) 303-335)
• Hamiltonian degree sequences in digraphs (with Daniela Kühn and Deryk Osthus, J. Combinatorial Theory Series B 100 (2010) 367-380)

• An Ore-type theorem for perfect packings in graphs (with Daniela Kühn and Deryk Osthus, SIAM Journal on Discrete Mathematics 23 (2009) 1335-1355)

• Enumerating solution-free sets in the integers (with Robert Hancock, Electronic Notes in Discrete Mathematics 56 (2016) 21-30)
• On a degree sequence analogue of Pósa’s conjecture (with Katherine Staden, Electronic Notes in Discrete Mathematics 49 (2015) 233-241)
• A sharp bound on the number of maximal sum-free sets (with József Balogh, Hong Liu and Maryam Sharifzadeh, Electronic Notes in Discrete Mathematics 49 (2015) 57-64)
• Tight minimum degree conditions forcing perfect matchings in uniform hypergraphs (with Yi Zhao, The Seventh European Conference on Combinatorics, Graph Theory and Applications, CRM Series Vol. 16 (2013) 33-38)
• Proof of the 1-factorization and Hamilton decomposition conjectures (with Béla Csaba, Daniela Kühn, Allan Lo and Deryk Osthus, The Seventh European Conference on Combinatorics, Graph Theory and Applications, CRM Series Vol. 16 (2013) 477-482)
• Matchings in 3-uniform hypergraphs of large minimum vertex degree (with Daniela Kühn and Deryk Osthus, Electronic Notes in Discrete Mathematics 38 (2011) 813-818)
• Degree sequences forcing Hamilton cycles in directed graphs (with Daniela Kühn and Deryk Osthus, Electronic Notes in Discrete Mathematics 34 (2009) 347-351)

• Embedding problems in graphs and hypergraphs (PhD thesis)
• The regularity lemma and applications to packings in graphs (MSci thesis)