Andrew Treglown Preprints and publications

• On degree sequences forcing the square of a Hamilton cycle (with Katherine Staden)
• A degree sequence Hajnal-Szemerédi theorem

• 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, to appear)
• The number of maximal sum-free subsets of integers (with József Balogh, Hong Liu and Maryam Sharifzadeh, Proceedings of the American Mathematical Society, to appear)
• On directed versions of the Hajnal-Szemerédi theorem (Combinatorics, Probability and Computing, to appear)

• 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)

• 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)