Dr Richard Mycroft PhD

Dr Richard Mycroft

School of Mathematics
Senior Lecturer

Contact details

School of Mathematics
University of Birmingham
B15 2TT

Richard Mycroft is a Senior Lecturer in Mathematics, whose research interests are primarily in the field of Extremal and Probabilistic Combinatorics. In particular, he has worked extensively on embeddings of graphs, directed graphs and hypergraphs. His programme of research is currently supported by an EPSRC Standard Grant ("Properties of Extremal and Random Hypergraphs", 2018-22), and was previously supported by an EPSRC First Grant (“Embeddings in Hypergraphs”, 2015-17).

Richard regularly publishes research papers in leading mathematics journals, with key publications including a proof for large tournaments of the well-known Sumner’s conjecture (dating from 1971), published in Proceedings of the LMS, and a geometric theory for hypergraph matching, giving wide-ranging sufficient conditions for the existence of perfect matchings in uniform hypergraphs, published in Memoirs of the AMS.

Richard enjoys communicating his work both in academic circles and to more general audiences. He regularly presents research at high-profile conferences both nationally and internationally, and has delivered many seminars at mathematics departments in the UK, US, Brazil, Austria and Hungary. Within the University of Birmingham, Richard currently lectures an introductory course in Combinatorics for first- and second-years and a third- and fourth-year course in Computation.

Since 2017 Richard has served as Academic Admissions Director for the School of Mathematics, playing a key role in undergraduate admissions activity.

For more information, please see Richard's School of Mathematics staff profile.


  • PhD in Pure Mathematics, University of Birmingham, 2010
  • MMath, University of Cambridge, 2007
  • BA (Hons) in Mathematics, University of Cambridge, 2006


Richard Mycroft read Mathematics at the University of Cambridge, gaining his BA (Hons) degree in 2006 and his MMath degree in 2007. Following this, he moved to the University of Birmingham to complete a PhD under the supervision of Deryk Osthus and Daniela Kühn. His thesis, submitted in 2010, was titled “The regularity method for directed graphs and hypergraphs”, with the most notable result being a proof for large tournaments of the well-known Sumner’s conjecture, which had been open since 1971.

Following the award of his PhD Richard moved to Queen Mary, University of London, where he spent a year working as a postdoctoral research assistant for Peter Keevash, with the primary focus of his research being the development of a geometric theory for perfect matchings in hypergraphs.

Richard then returned to the University of Birmingham in June 2011 to take up a lectureship in Mathematics. Since then he has continued active research in extremal graph theory, particularly relating to hypergraphs. In 2017 he was promoted to Senior Lecturer.


Richard is currently lecturing the Combinatorics half of the 1AC Algebra and Combinatorics module, available for first- and second-year students, and the Computation half of the 3RC Randomness and Computation module, available for third- and fourth-year students. These modules are available to students studying the G100 BSc Mathematics and G103 MSci Mathematics programmes, as well as a range of other programmes.

Postgraduate supervision

Richard Mycroft has acted as principal supervisor for four PhD students, and as co-supervisor for a further five PhD students. He is always keen to hear from any prospective students who are interested in PhD study in Combinatorics.


Richard’s research interests lie in the field of Combinatorics, and more specifically in the area of extremal graph theory. In particular he has worked extensively on embedding problems relating to hypergraphs, centred around the development of a geometric theory of perfect matchings in uniform hypergraphs, with multiple subsequent applications both in his own work and the work of other researchers. Other highlights of Richard's research include a random version of Sperner's theorem on antichains, a multipartite version of the Hajnal-Szemerédi theorem and a proof of the well-known Sumner's conjecture (dating to 1971) for directed trees in large tournaments.

From 2018 to 2022 Richard's programme of research is being supported by a £295k EPSRC Standard Grant for a project titled `Properties of Extremal and Random Hypergraphs'; previously his research was supported from 2015 to 2017 by a £124k EPSRC First Grant for a project titled `Embeddings in Hypergraphs'.


Recent publications


Bowtell, C & Mycroft, R 2019, 'Classification of Maximum Hittings by Large Families', Graphs and Combinatorics, vol. 36, pp. 27-39. https://doi.org/10.1007/s00373-019-02115-1

Garbe, F, McDowell, A & Mycroft, R 2018, 'Contagious sets in a degree-proportional bootstrap percolation process', Random Structures and Algorithms, vol. 53, no. 4, pp. 638-651. https://doi.org/10.1002/rsa.20818

Garbe, F & Mycroft, R 2018, 'Hamilton cycles in hypergraphs below the Dirac threshold', Journal of Combinatorial Theory. Series B. https://doi.org/10.1016/j.jctb.2018.04.010

McDowell, A & Mycroft, R 2018, 'Hamilton ℓ-Cycles in Randomly Perturbed Hypergraphs', Electronic Journal of Combinatorics, vol. 25, no. 4, P4.36. <http://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p36>

Balogh, J, McDowell, A, Molla, T & Mycroft, R 2018, 'Triangle-tilings in graphs without large independent sets', Combinatorics, Probability and Computing. https://doi.org/10.1017/S0963548318000196

Mycroft, R & Naia Dos Santos, T 2018, 'Unavoidable trees in tournaments', Random Structures and Algorithms. https://doi.org/10.1002/rsa.20765

Martin, R, Mycroft, R & Skokan, J 2017, 'An asymptotic multipartite Kühn-Osthus theorem', SIAM Journal on Discrete Mathematics, vol. 31, no. 3, pp. 1498-1513. https://doi.org/10.1137/16M1070621

Cooley, O & Mycroft, R 2017, 'The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph', Discrete Mathematics, vol. 340, no. 6, pp. 1172-1179. https://doi.org/10.1016/j.disc.2016.12.015

Allen, P, Böttcher, J, Cooley, O & Mycroft, R 2017, 'Tight cycles and regular slices in dense hypergraphs', Journal of Combinatorial Theory, Series A, vol. 149, pp. 30-100. https://doi.org/10.1016/j.jcta.2017.01.003

Lenz, J, Mubayi, D & Mycroft, R 2016, 'Hamilton cycles in quasirandom hypergraphs', Random Structures and Algorithms. https://doi.org/10.1002/rsa.20638

Mycroft, R 2016, 'Packing k-partite k-uniform hypergraphs', Journal of Combinatorial Theory, Series A, vol. 138, pp. 60-132. https://doi.org/10.1016/j.jcta.2015.09.007

Keevash, P & Mycroft, R 2015, 'A Multipartite Hajnal-Szemerédi Theorem', Journal of Combinatorial Theory. Series B, vol. 114, pp. 187-236. https://doi.org/10.1016/j.jctb.2015.04.003

Keevash, P, Knox, F & Mycroft, R 2015, 'Polynomial-time perfect matchings in dense hypergraphs', Advances in Mathematics, vol. 269, pp. 265-334. https://doi.org/10.1016/j.aim.2014.10.009


Keevash, P & Mycroft, R 2015, A geometric theory for hypergraph matching. in A geometric theory for hypergraph matching. vol. 233, Chapter 6, American Mathematical Society. https://doi.org/10.1090/memo/1098

Conference contribution

Garbe, F & Mycroft, R 2016, The Complexity of the Hamilton Cycle Problem in Hypergraphs of High Minimum Codegree. in N Ollinger & H Vollmer (eds), 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). vol. 47, 38, Leibniz International Proceedings in Informatics (LIPIcs), vol. 47, Schloss Dagstuhl, Dagstuhl, Germany, pp. 1-13. https://doi.org/10.4230/LIPIcs.STACS.2016.38

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