School of Mathematics
,
University of Birmingham
Andrew Treglown
Preprints and publications
Books edited:
Surveys in Combinatorics 2019
(joint editor with Allan Lo, Richard Mycroft and Guillem Perarnau)
Preprints:
On some extremal and probabilistic questions for tree posets
(with
Balázs Patkós
)
Tiling edge-ordered graphs with monotone paths and other structures
(with Igor Araujo,
Simón Piga
and Zimu Xiang)
On oriented cycles in randomly perturbed digraphs
(with Igor Araujo,
József Balogh
, Robert A. Krueger and
Simón Piga
)
Accepted papers:
The induced saturation problem for posets
(with
Andrea Freschi
,
Simón Piga
and Maryam Sharifzadeh, to appear in Combinatorial Theory)
Papers:
2022
Dirac-type results for tilings and coverings in ordered graphs
(with
Andrea Freschi
, Forum of Mathematics, Sigma, 10 (2022) e104, 41 pages)
Complete subgraphs in a multipartite graph
(with
Allan Lo
and
Yi Zhao
, Combinatorics, Probability and Computing, 31 (2022) 1092-1101)
An asymmetric random Rado theorem for single equations: the 0-statement
(with
Robert Hancock
, Random Structures and Algorithms, 60 (2022) 529-550)
On maximal sum-free sets in abelian groups
(with Nathanaël Hassler, Electronic Journal of Combinatorics, 29 (2022) #P2.32, 24 pages)
On deficiency problems for graphs
(with
Andrea Freschi
and
Joseph Hyde
, Combinatorics, Probability and Computing, 31 (2022) 478-488)
Tilings in vertex ordered graphs
(with
József Balogh
and
Lina Li
, J. Combinatorial Theory Series B, 155 (2022) 171-201)
Extremal problems for multigraphs
(with A. Nicholas Day and
Victor Falgas-Ravry
, J. Combinatorial Theory Series B, 154 (2022) 1-48)
2021
A note on color-bias Hamilton cycles in dense graphs
(with
Andrea Freschi
,
Joseph Hyde
and Joanna Lada, SIAM Journal on Discrete Mathematics, 35 (2021) 970-975)
A discrepancy version of the Hajnal-Szemerédi theorem
(with
József Balogh
,
Béla Csaba
and
András Pluhár
, Combinatorics, Probability and Computing, 30 (2021) 444-459)
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, 58 (2021) 480-516)
Transitive tournament tilings in oriented graphs with large minimum total degree
(with
Allan Lo
,
Louis DeBiasio
and
Theo Molla
, SIAM Journal on Discrete Mathematics, 35 (2021) 250-266)
2020
Ramsey properties of randomly perturbed graphs: cliques and cycles
(with
Shagnik Das
, Combinatorics, Probability and Computing, 29 (2020) 830-867)
The bandwidth theorem for locally dense graphs
(with
Katherine Staden
, Forum of Mathematics, Sigma 8 (2020) e42, 36 pages)
Existence thresholds and Ramsey properties of random posets
(with
Victor Falgas-Ravry
,
Klas Markström
and
Yi Zhao
, Random Structures and Algorithms 57 (2020) 1097-1133)
Vertex Ramsey properties of randomly perturbed graphs
(with
Shagnik Das
and Patrick Morris, Random Structures and Algorithms 57 (2020) 983-1006)
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)
2019
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)
2018
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)
2017
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)
2016
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)
2015
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)
2014
A random version of Sperner's theorem
(with
József Balogh
and
Richard Mycroft
, J. Combinatorial Theory Series A, 128 (2014) 104-110)
2013
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)
2012
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)
2010
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)
2009
An Ore-type theorem for perfect packings in graphs
(with
Daniela Kühn
and
Deryk Osthus
, SIAM Journal on Discrete Mathematics 23 (2009) 1335-1355)
Conference papers:
Tiling problems in edge-ordered graphs
(with Igor Araujo,
Simón Piga
and Zimu Xiang, Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications, EUROCOMB’23)
Cycles of every length and orientation in randomly perturbed digraphs
(with Igor Araujo,
József Balogh
, Robert A. Krueger and
Simón Piga
, Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications, EUROCOMB’23)
A general bound for the induced poset saturation problem
(with
Andrea Freschi
,
Simón Piga
and Maryam Sharifzadeh, Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications, EUROCOMB’23)
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)
Other publications:
Embedding problems in graphs and hypergraphs
(PhD thesis)
The regularity lemma and applications to packings in graphs
(MSci thesis)