Dr Allan Lo PhD

Dr Allan Lo

School of Mathematics
Senior Lecturer

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT

Allan Lo is a Senior Lecturer, whose research interests lie primarily in combinatorics, in particular, in extremal graph theory and hypergraphs. He is currently investigating Ramsey-type problems in hypergraphs. 

For more information, visit Allan's School webpage.


Senior Lecture in Pure Mathematics

  • PhD (Mathematics, Cambridge 2010)
  • MA (Mathematics, Cambridge 2006)
  • BA (Mathematics, Cambridge 2005)


Allan Lo received his PhD degree from the University of Cambridge in 2010 under the supervision of Professor Andrew Thomason. He was a postdoctoral position at Umeå University, Sweden. He then joined School of Mathematics at the University of Birmingham in 2011 as a research fellow. In 2014, he became a Birmingham Fellow. He became a Senior Lecturer since 2019.

Postgraduate supervision

  • Nicolás Sanhueza-Matamala 2015-9
  • Vincent Pfenninger 2018-Present

Allan Lo is happy to hear from any students who are interested in PhD study in Combinatorics.


Research Theme

Combinatorics, especially Extremal Graph Theory and Hypergraphs

Research Activities

The main research area of Allan Lo is Combinatorics. He has worked on extremal graph theory, hypergraphs and Ramsey theory.

For example, he studied edge-decomposition of graphs. Typical questions in this field also arise from considering scheduling problems, a famous recreational example being Kirkman's schoolgirl problem which dates back to 1850 and asks for an assignment of 15 schoolgirls into groups of 3 on 7 different days such that no two schoolgirls are allocated to the same group more than once.

This particular problem is easy to solve and its solution is the simplest example of a Steiner triple system or, more generally, a combinatorial design. More general constructions of such combinatorial designs are often based on geometric and algebraic concepts such as projective planes and Hadamard matrices.


Recent publications


DeBiasio, L, Lo, A, Molla, T & Treglown, A 2021, 'Transitive tournament tilings in oriented graphs with large minimum total degree', SIAM Journal on Discrete Mathematics, vol. 35, no. 1, pp. 250–266. https://doi.org/10.1137/19M1269257

Han, J, Lo, A & Sanhueza-Matamala, N 2020, 'Covering and tiling hypergraphs with tight cycles', Combinatorics, Probability and Computing, vol. 0, pp. 1-36. https://doi.org/10.1017/S0963548320000449

Barber, B, Kuhn, D, Lo, A, Montgomery, R & Osthus, D 2020, 'Minimalist designs', Random Structures and Algorithms.

Lang, R & Lo, A 2020, 'Monochromatic cycle partitions in random graphs', Combinatorics, Probability and Computing. https://doi.org/10.1017/S0963548320000401

Glock, S, Kuhn, D, Lo, A & Osthus, D 2020, 'On a conjecture of Erdős on locally sparse Steiner triple systems', Combinatorica, vol. 40, no. 3, pp. 363-403. https://doi.org/10.1007/s00493-019-4084-2

Glock, S, Kuhn, D, Lo, A & Osthus, D 2020, 'The existence of designs via iterative absorption: hypergraph F-designs for arbitrary F', Memoirs of the American Mathematical Society. <https://arxiv.org/pdf/1611.06827>

Lo, A & Sanhueza Matamala, N 2019, 'An asymptotic bound for the strong chromatic number', Combinatorics, Probability and Computing, vol. 28, no. 5, pp. 768-776. https://doi.org/10.1017/S0963548318000561

Lo, A, Patel, V, Skokan, J & Talbot, J 2019, 'Decomposing tournaments into paths', Proceedings of the London Mathematical Society.

Lo, A 2019, 'Long properly coloured cycles in edge-coloured graphs', Journal of Graph Theory, vol. 90, no. 3, pp. 416-442. https://doi.org/10.1002/jgt.22405

Glock, S, Kühn, D, Lo, A, Montgomery, R & Osthus, D 2019, 'On the decomposition threshold of a given graph', Journal of Combinatorial Theory. Series B, vol. 139, pp. 47-127. https://doi.org/10.1016/j.jctb.2019.02.010

DeBiasio, L & Lo, A 2019, 'Spanning trees with few branch vertices', SIAM Journal on Discrete Mathematics, vol. 33, no. 3, pp. 1503–1520. https://doi.org/10.1137/17M1152759

Lo, A & Zhao, Y 2018, 'Codegree Turán density of complete $r$-uniform hypergraphs', SIAM Journal on Discrete Mathematics, vol. 32, no. 2, pp. 1154-1158. https://doi.org/10.1137/18M1163956

Lo, A, Sanhueza-Matamala, N & Wang, G 2018, 'Density of monochromatic infinite paths', Electronic Journal of Combinatorics, vol. 25, no. 4, P4.29. <http://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p29>

Lo, A & Patel, V 2018, 'Hamilton cycles in sparse robustly expanding digraphs', Electronic Journal of Combinatorics, vol. 25, no. 3, #P3.44. <https://arxiv.org/pdf/1507.04472>

Falgas-Ravry, V & Lo, A 2018, 'Subgraphs with large minimum ℓ-degree in hypergraphs where almost all ℓ-degrees are large', The Electronic Journal of Combinatorics, vol. 25, no. 2, P2.18. <http://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i2p18>

View all publications in research portal