Dr Andrew Treglown is a Birmingham Fellow, having previously worked as a Research Fellow at Queen Mary, University of London and Charles University, Prague.
Andrew is a member of the Combinatorics group. His research interests mainly focus on extremal and probabilistic graph theory.
Andrew has a number of international collaborative links, particularly with various institutions in the USA. He regularly gives talks at international conferences and has been invited to give a number of seminars across Europe and in the USA.
School web page: http://web.mat.bham.ac.uk/~treglowa
PhD in Pure Mathematics, University of Birmingham, 2011
MSci in Mathematical Sciences, University of Birmingham, 2007
Andrew Treglown received an MSci from Birmingham in 2007, followed by a PhD in 2011. After research fellowships at Queen Mary, University of London and Charles University, Prague, he re-joined the School of Mathematics here in Birmingham in September 2013.
Andrew Treglown is interested in supervising PhD students in Combinatorics. If you are interested, please email him.
Extremal graph theory
Hypergraphs and directed graphs
Andrew’s primary research interests lie in extremal graph theory. His most recent work has been on graph decompositions. In particular, together with B. Csaba, D. Kühn, A. Lo and D. Osthus, he has solved the beautiful 1-factorization conjecture for large graphs (see http://en.wikipedia.org/wiki/1-factorization_conjecture#1-factorization_conjecture).
This classical conjecture gives a condition for a regular graph to have a decomposition into perfect matchings.
One of the most central results in Ramsey theory is Goodman’s theorem from 1959 which determines the minimum number of monochromatic triangles in a 2-coloured complete graph. Recently, Andrew and his co-authors (J. Cummings, D. Kral, F. Pfender, K. Sperfeld and M. Young) have solved this problem for 3-coloured graphs, thereby solving a classical problem of Goodman.
Andrew has also written a number of papers on (hyper)graph embedding problems. For example, in a sequence of several papers, he and his co-authors (D. Kühn, D. Osthus and Y. Zhao) have established a number of minimum degree conditions that ensure a hypergraph contains a perfect matching.
For a complete list of publications, visit http://web.mat.bham.ac.uk/~treglowa/pubat.html
Kühn, D., Osthus, D., Treglown, A. (2009), An Ore-type theorem for perfect packings in graphs, SIAM Journal on Discrete Mathematics, 23: 1335-1355
Kühn, D., Osthus, D., Treglown, A. (2010), Hamiltonian degree sequences in digraphs, Journal of Combinatorial Theory Series B, 100: 367-380
Kühn, D., Osthus, D., Treglown, A. (2010), Hamilton decompositions of regular tournaments, Proceedings of the London Mathematical Society, 101: 303-335
Knox, F., Treglown, A., (2013) Embedding spanning bipartite graphs of small bandwidth, Combinatorics, Probability and Computing, 22: 71-96
Treglown, A., Zhao, Y. (2013), Exact minimum degree thresholds for perfect matchings in uniform hypergraphs II,
Journal of Combinatorial Theory Series A, 120: 1463-1482
Kühn, D., Osthus, D., Treglown, A. (2013), Matchings in 3-uniform hypergraphs, Journal of Combinatorial Theory Series B, 103: 291-305
Cummings, J., Kral, D., Pfender, F., Sperfeld, K., Treglown, A., Young, M. (2013), Monochromatic triangles in three-coloured graphs, Journal of Combinatorial Theory Series B, 103: 489-503