## John HaslegraveResearch Associate |

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.

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.

- J. Haslegrave, J. Jordan & M. Yarrow:
*Competing types in preferential attachment graphs with community structure*. arXiv - J. Haslegrave:
*Monitoring edge-geodetic sets: hardness and graph products*. arXiv - S. Akbari, J. Haslegrave, M. Javadi, N. Nahvi & H. Niaparast:
*Tight bounds on the chromatic edge stability index of graphs*. arXiv - S. Cambie, J. Haslegrave & R. J. Kang:
*When removing an independent set is optimal for reducing the chromatic number*. arXiv - J. Haslegrave:
*Determining triangulations and quadrangulations by boundary distances*. arXiv

- J. Haslegrave:
*Sum index, difference index and exclusive sum number of graphs*, Graphs and Combinatorics. arXiv - J. Haslegrave, J. Hyde,
J. Kim & H. Liu:
*Ramsey numbers of cycles versus general graphs*, Forum of Mathematics, Sigma. arXiv

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

- J. Haslegrave, J. Kim & H. Liu:
*Extremal density for sparse minors and subdivisions*, Extended Abstracts EuroComb 2021. book - A. Georgakopoulos, J. Haslegrave, T. Sauerwald & J. Sylvester:
*Choice and bias in random walks*, Innovations in Theoretical Computer Science 2020. proceedings (OA)