Jonathan Noel

About Me

I am an Assistant Professor in the Department of Mathematics and Statistics at the University of Victoria. I am a member of the Discrete Mathematics Group.

Here is my CV and my Google Scholar profile.

Research Interests

• Limits of combinatorial objects

• Quasirandomness

• Extremal combinatorics

• Probabilistic combinatorics

• Ramsey theory

• Bootstrap percolation

• Graph colourings and homomorphisms

• Computational complexity

See my list of recorded research talks.


Job Opportunity: Postdoctoral Fellowship in Combinatorics

Natasha Morrison and I are seeking candidates to nominate for a PIMS Postdoctoral Fellowship to be held at the University of Victoria starting in 2024. Click the link for more details!

Research Papers

Topics: Extremal Combinatorics , Probabilistic Combinatorics , Combinatorial Limits , Bootstrap Percolation , Graph Colouring , Theoretical Computer Science , Other , check all , uncheck all


32. Turán Colourings in Off-Diagonal Ramsey Multiplicity (with Joseph Hyde and Jae-baek Lee). Soon to be Submitted. (ext)

31. Off-Diagonal Commonality of Graphs via Entropy (with Natalie Behague and Natasha Morrison). Submitted. (ext/lim)

30. Off-Diagonal Ramsey Multiplicity (with Elena Moss). Soon to be Submitted. (ext/lim)

29. Sidorenko-Type Inequalities for Pairs of Trees (with Natalie Behague, Gabriel Crudele and Lina M. Simbaqueba). Submitted. (ext/pr)

28. Disconnected Common Graphs via Supersaturation (with Jae-baek Lee). Submitted. (ext/lim)

27. Six Permutation Patterns Force Quasirandomness (with Gabriel Crudele and Peter J. Dukes). Submitted. (pr/lim)

26. Common Pairs of Graphs (with Natalie Behague and Natasha Morrison). Submitted. (ext/lim)

25. Circle Squaring with Pieces of Small Boundary and Low Borel Complexity (with András Máthé and Oleg Pikhurko). Submitted. (other) Quanta Magazine article. Popular Mechanics article. Discover Magazine article.

Published, to Appear or Accepted

24. Extremal Bounds for Three-Neighbour Bootstrap Percolation in Dimensions Two and Three (with Peter J. Dukes and Abel E. Romer). SIAM J. Discrete Math. 37 (3) (2023) 2088–2125.(ext/boot)

23. On the Running Time of Hypergraph Bootstrap Percolation (with Arjun Ranganathan). Electron. J. Combin. 30 (2) (2023) #2.46. (ext/boot)

22. Density maximizers of layered permutations (with Adam Kabela, Daniel Kráľ and Théo Pierron). Electron. J. Combin. 29 (3) (2022) #3.56. (ext/lim)

21. Recolouring homomorphisms to triangle-free reflexive graphs (with Jae-baek Lee and Mark Siggers). Journal of Algebraic Combinatorics (2022) 21 pages. (tcs/col)

20. Non-bipartite k-common graphs (with Daniel Kráľ, Sergey Norin, Jan Volec and Fan Wei). Combinatorica 42, (2022) 87-114. (ext/lim)

19. Pirates in Wonderland: Liquid Democracy has Bicritical Guarantees (with Mashbat Suzuki and Adrian Vetta). SAGT 2021: Algorithmic Game Theory 391-405. (tcs)

18. A Sharp Threshold for Bootstrap Percolation in a Random Hypergraph (with Natasha Morrison). Electron. J. Probab. 26 (2021) 1-85 (pr/boot)

17. Cyclic Coloring of Plane Graphs with Maximum Face Size 16 and 17 (with Zdeněk Dvořák, Michael Hebdige, Filip Hlásek and Daniel Kráľ). European J. Combin. 94 (2021) 103287 (col)

16. Bounding the number of cycles in a graph in terms of its degree sequence (with Zdeněk Dvořák, Natasha Morrison, Sergey Norin and Luke Postle). European J. Combin. 91 (2021) 103206 (ext)

15. Cycles of length three and four in tournaments (with Timothy F. N. Chan, Andrzej Grzesik and Daniel Kráľ). J. Combin. Theory Ser. A. 175 (2020) 105276 (ext/lim)

14. Characterization of quasirandom permutations by a pattern sum (with Timothy F. N. Chan, Daniel Kráľ, Yanitsa Pehova, Maryam Sharifzadeh and Jan Volec). Random Structures & Algorithms 57(4) (2020) 920--939. (pr/lim)

13. Reconfiguring Graph Homomorphisms on the Sphere (with Jae-baek Lee and Mark Siggers). European J. Combin. 86 (2020) 103086. (tcs/col)

12. Graph Homomorphism Reconfiguration and Frozen H-Colourings (with Richard C. Brewster, Jae-baek Lee, Benjamin Moore and Mark Siggers). J. Graph Theory 94 (3) (2020) 398--420. (tcs/col)

11. Finitely forcible graphons with an almost arbitrary structure (with Daniel Kráľ, László Miklós Lovász and Jakub Sosnovec). Discrete Anal. Paper 9 (2019) 36 pages. (ext/lim)

10. Extremal Bounds for Bootstrap Percolation in the Hypercube (with Natasha Morrison). J. Combin. Theory Ser. A 156 (2018) 61--84. (ext/boot)

9. Weak regularity and finitely forcible graph limits (with Jacob W. Cooper, Tomáš Kaiser and Daniel Kráľ). Trans. Amer. Math. Soc. 370 (6) (2018) 3833--3864. (ext/lim)

8. Supersaturation in Posets and Applications Involving the Container Method (with Alex Scott and Benny Sudakov). J. Combin. Theory Ser. A 154 (2018) 247--284. (ext/pr)

7. Saturation in the Hypercube and Bootstrap Percolation (with Natasha Morrison and Alex Scott). Combin. Probab. Comput. 26 (1) (2017) 78--98. (ext/boot)

6. A Dichotomy Theorem for Circular Colouring Reconfiguration (with Richard C. Brewster, Sean McGuinness and Benjamin Moore). Theoret. Comput. Sci. (639) (2016) 1--13. (tcs/col)

5. Mixing Homomorphisms, Recolorings, and Extending Circular Precolorings (with Richard C. Brewster). J. Graph Theory 80 (3) (2015) 173--198. (col)

4. A Proof of a Conjecture of Ohba (with Bruce A. Reed and Hehui Wu). J. Graph Theory 79 (2) (2015) 86--102. (col)

3. Beyond Ohba's Conjecture: A bound on the choice number of k-chromatic graphs with n vertices (with Douglas B. West, Hehui Wu and Xuding Zhu). European J. Combin. 43 (2015) 295--305. (col)

2. On Saturated k-Sperner Systems (with Natasha Morrison and Alex Scott). Electron. J. Combin. 21 (3) (2014) #P3.22. (ext)

1. Extending precolourings of circular cliques (with Richard C. Brewster). Discrete Math. 312 (1) (2012) 35--41. (col)

Education and Theses

DPhil (PhD) Mathematics
University of Oxford
Defended: June 17, 2016
DPhil Thesis: Extremal Combinatorics, Graph Limits and Computational Complexity
Adviser: Alex Scott

M.Sc. Mathematics
McGill University
April 2013
Masters Thesis: Choosability of Graphs with Bounded Order: Ohba's Conjecture and Beyond
Adviser: Bruce Reed

B.Sc. (Hons) Mathematics
Thompson Rivers University
April 2011
Honours Thesis: The Invariant Subspace Problem
Adviser: Robb Fry