John Haslegrave  

John Haslegrave

Research Associate
Mathematical Institute, University of Oxford

Office: N2.04
Phone: +44 (0)1865 273538

Page last modified 24th September 2022.


I recently moved to Oxford from Warwick, to work with Peter Keevash on the ERC project "Combinatorial Applications of Random Processes and Expansion".

In January and May 2022 I visited the Probability Group at the University of Sheffield.

Seminars and talks

I will be speaking at the University of Bristol Combinatorics Seminar on Tuesday 29th November. Earlier in 2022 I spoke at the University of Geneva Mathematical Physics Seminar, the Random Networks Workshop in Sheffield and the University of Oxford Combinatorial Theory Seminar.

I spoke at the Chris Cannings Memorial Symposium in 2019. Chris had wide-ranging interests in random processes, evolutionary games, and games on graphs, but was also very influential in the field of statistical genetics. He was a joy to work with, and had a great sense of humour. Here is a picture of the participants, taken by Mark Yarrow.


My main research interests are random graphs, random walks, interacting particle systems and extremal problems on graphs and hypergraphs. I previously worked with Hong Liu on the UKRI project Embeddings in Sparse Graphs, and with Agelos Georgakopoulos on the ERC project Random Graph Geometry and Convergence. I have a Google Scholar profile. My MathSciNet profile is here.

I have an Erdős number of three, by several different routes. My Erdős number of the second kind (only two-author papers count) is also three, but in this case the route is unique: John Haslegrave — Itai Benjamini — László Lovász — Paul Erdős.

Below are links to the journal versions of published papers and arXiv preprints for those not yet published. Where the journal version is not open access, both are provided.

Submitted for publication

To appear

  1. J. Haslegrave, J. Hu, J. Kim, H. Liu, B. Luan & G. Wang: Crux and long cycles in graphs, SIAM Journal on Discrete Mathematics. arXiv
  2. J. Haslegrave, J. Kim & H. Liu: Extremal density for sparse minors and subdivisions, International Mathematics Research Notices. journal (OA)
  3. J. Haslegrave: Countable graphs are majority 3-choosable, Discussiones Mathematicae Graph Theory. journal (OA)


  1. S. Cambie & J. Haslegrave: On the relationship between variable Wiener index and variable Szeged index, Applied Mathematics and Computation 431 (2022). journal (OA)
  2. J. Haslegrave: The number and average size of connected sets in graphs with degree constraints, Journal of Graph Theory 100:3 (2022). journal (OA)
  3. I. Benjamini & J. Haslegrave: Degrees in link graphs of regular graphs, Electronic Journal of Combinatorics 29:2 (2022). journal (OA)
  4. J. Haslegrave, T. Sauerwald & J. Sylvester: Time dependent biased random walks, ACM Transactions on Algorithms 18:2 (2022). journal arXiv
  5. A. Georgakopoulos, J. Haslegrave, R. Montgomery & B. Narayanan: Spanning surfaces in 3-graphs, Journal of the European Mathematical Society 24:1 (2022). journal arXiv
  6. J. Haslegrave: The path minimises the average size of a connected induced subgraph, Discrete Mathematics 345:5 (2022). journal (OA)
  7. A. Georgakopoulos, J. Haslegrave, T. Sauerwald & J. Sylvester: The power of two choices in random walks, Combinatorics, Probability and Computing 31:1 (2022). journal (OA)
  8. A. Georgakopoulos & J. Haslegrave: A time-invariant random graph with splitting events, Electronic Communications in Probability 26 (2021). journal (OA)
  9. J. Haslegrave, V. Sidoravicius & L. Tournier: Three-speed ballistic annihilation: phase transition and universality, Selecta Mathematica 27 (2021). journal arXiv
    Dedicated to Vladas Sidoravicius, who sadly passed away shortly after this work was completed.
  10. J. Haslegrave & L. Tournier: Combinatorial universality in three-speed ballistic annihilation, in In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, Progress in Probability 77 (2021). arXiv
  11. J. Haslegrave & C. Panagiotis: Site percolation and isoperimetric inequalities for plane graphs, Random Structures and Algorithms 58:1 (2021). journal (OA)
  12. A. Georgakopoulos & J. Haslegrave: Percolation on an infinitely generated group, Combinatorics, Probability and Computing 29:4 (2020). journal arXiv
  13. J. Haslegrave, J. Jordan & M. Yarrow: Condensation in preferential attachment models with location-based choice, Random Structures and Algorithms 56:3 (2020). journal arXiv
  14. R. Henze, C. Mu, et al.: Multi-scale stochastic organization-oriented coarse-graining exemplified on the human mitotic checkpoint, Scientific Reports 9 (2019). journal (OA)
  15. A. Georgakopoulos, J. Haslegrave & R. Montgomery: Forcing large tight components in 3-graphs, European Journal of Combinatorics 77 (2019). journal arXiv
  16. J. Haslegrave & J. Jordan: Non-convergence of proportions of types in a preferential attachment graph with three co-existing types, Electronic Communications in Probability 23 (2018). journal (OA)
    Dedicated to our late friend and colleague Chris Cannings.
  17. J. Haslegrave: Proof of a local antimagic conjecture, Discrete Mathematics and Theoretical Computer Science 20:1 (2018). journal (OA)
  18. J. Haslegrave, R. A. B. Johnson & S. Koch: Locating a robber with multiple probes, Discrete Mathematics 341:1 (2018). journal (OA)
  19. J. Haslegrave & M. Puljiz: Reaching consensus on a connected graph, Journal of Applied Probability 54:1 (2017). journal arXiv
  20. J. Haslegrave & C. Cannings: Majority dynamics with one nonconformist, Discrete Applied Mathematics 219 (2017). journal (OA)
  21. J. Haslegrave, R. A. B. Johnson & S. Koch: Subdivisions in the robber-locating game, Discrete Mathematics 339:11 (2016). journal (OA)
  22. J. Haslegrave & J. Jordan: Preferential attachment with choice, Random Structures and Algorithms 48:4 (2016). journal arXiv
  23. J. Haslegrave, R. A. B. Johnson & S. Koch: The robber-locating game, Discrete Mathematics 339:1 (2016). journal (OA)
  24. J. Haslegrave: Judicious partitions of uniform hypergraphs, Combinatorica 34:5 (2014). journal arXiv
  25. J. Haslegrave: Bounds on Herman's algorithm, Theoretical Computer Science 550 (2014). journal (OA)
  26. J. Haslegrave: Extremal results on average subtree density of series-reduced trees, Journal of Combinatorial Theory series B 107 (2014). journal (OA)
  27. J. Haslegrave: An evasion game on a graph, Discrete Mathematics 314 (2014). journal (OA)
  28. J. Haslegrave: The Bollobás–Thomason conjecture for 3-uniform hypergraphs, Combinatorica 32:4 (2012). journal arXiv

Conference proceedings