John Haslegrave  

John Haslegrave

Research Associate
Mathematical Institute, University of Oxford

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

Page last modified 14th March 2023.

  Non-convergence in preferential attachment with two types and three communities  


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

In 2022 I spoke at the University of Bristol Combinatorics Seminar, 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. Here are my MathSciNet profile and my zbMATH profile.

I have an Erdős number of 3, by several different routes. My Erdős number of the second kind (only two-author papers count) is also 3, 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


  1. J. Haslegrave: Sum index, difference index and exclusive sum number of graphs, Graphs and Combinatorics 39:2 (2023). journal (OA)
  2. J. Haslegrave, J. Hyde, J. Kim & H. Liu: Ramsey numbers of cycles versus general graphs, Forum of Mathematics, Sigma 11 (2023). journal (OA)
  3. J. Haslegrave: Countable graphs are majority 3-choosable, Discussiones Mathematicae Graph Theory 43:2 (2023). journal (OA)
  4. J. Haslegrave, J. Hu, J. Kim, H. Liu, B. Luan & G. Wang: Crux and long cycles in graphs, SIAM Journal on Discrete Mathematics 36:4 (2022). journal arXiv
  5. J. Haslegrave, J. Kim & H. Liu: Extremal density for sparse minors and subdivisions, International Mathematics Research Notices 2022:20 (2022). journal (OA)
  6. S. Cambie & J. Haslegrave: On the relationship between variable Wiener index and variable Szeged index, Applied Mathematics and Computation 431 (2022). journal (OA)
  7. J. Haslegrave: The number and average size of connected sets in graphs with degree constraints, Journal of Graph Theory 100:3 (2022). journal (OA)
  8. I. Benjamini & J. Haslegrave: Degrees in link graphs of regular graphs, Electronic Journal of Combinatorics 29:2 (2022). journal (OA)
  9. J. Haslegrave, T. Sauerwald & J. Sylvester: Time dependent biased random walks, ACM Transactions on Algorithms 18:2 (2022). journal arXiv
  10. A. Georgakopoulos, J. Haslegrave, R. Montgomery & B. Narayanan: Spanning surfaces in 3-graphs, Journal of the European Mathematical Society 24:1 (2022). journal arXiv
  11. J. Haslegrave: The path minimises the average size of a connected induced subgraph, Discrete Mathematics 345:5 (2022). journal (OA)
  12. 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)
  13. A. Georgakopoulos & J. Haslegrave: A time-invariant random graph with splitting events, Electronic Communications in Probability 26 (2021). journal (OA)
  14. 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.
  15. 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
  16. J. Haslegrave & C. Panagiotis: Site percolation and isoperimetric inequalities for plane graphs, Random Structures and Algorithms 58:1 (2021). journal (OA)
  17. A. Georgakopoulos & J. Haslegrave: Percolation on an infinitely generated group, Combinatorics, Probability and Computing 29:4 (2020). journal arXiv
  18. J. Haslegrave, J. Jordan & M. Yarrow: Condensation in preferential attachment models with location-based choice, Random Structures and Algorithms 56:3 (2020). journal arXiv
  19. 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)
  20. A. Georgakopoulos, J. Haslegrave & R. Montgomery: Forcing large tight components in 3-graphs, European Journal of Combinatorics 77 (2019). journal (OA)
  21. 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.
  22. J. Haslegrave: Proof of a local antimagic conjecture, Discrete Mathematics and Theoretical Computer Science 20:1 (2018). journal (OA)
  23. J. Haslegrave, R. A. B. Johnson & S. Koch: Locating a robber with multiple probes, Discrete Mathematics 341:1 (2018). journal (OA)
  24. J. Haslegrave & M. Puljiz: Reaching consensus on a connected graph, Journal of Applied Probability 54:1 (2017). journal arXiv
  25. J. Haslegrave & C. Cannings: Majority dynamics with one nonconformist, Discrete Applied Mathematics 219 (2017). journal (OA)
  26. J. Haslegrave, R. A. B. Johnson & S. Koch: Subdivisions in the robber-locating game, Discrete Mathematics 339:11 (2016). journal (OA)
  27. J. Haslegrave & J. Jordan: Preferential attachment with choice, Random Structures and Algorithms 48:4 (2016). journal arXiv
  28. J. Haslegrave, R. A. B. Johnson & S. Koch: The robber-locating game, Discrete Mathematics 339:1 (2016). journal (OA)
  29. J. Haslegrave: Judicious partitions of uniform hypergraphs, Combinatorica 34:5 (2014). journal arXiv
  30. J. Haslegrave: Bounds on Herman's algorithm, Theoretical Computer Science 550 (2014). journal (OA)
  31. J. Haslegrave: Extremal results on average subtree density of series-reduced trees, Journal of Combinatorial Theory series B 107 (2014). journal (OA)
  32. J. Haslegrave: An evasion game on a graph, Discrete Mathematics 314 (2014). journal (OA)
  33. J. Haslegrave: The Bollobás–Thomason conjecture for 3-uniform hypergraphs, Combinatorica 32:4 (2012). journal arXiv

Conference proceedings