James Davies

Publications

Submitted or Accepted

31. Counterexample to the conjectured coarse grid theorem, https://arxiv.org/abs/2508.15342, submitted (with Sandra Albrechtsen)

30. Binary matroids and degree-boundedness for pivot-minors, https://arxiv.org/abs/2507.23182, submitted (with Rutger Campbell, and Robert Hickingbotham)

29. Odd coloring graphs with linear neighborhood complexity, https://arxiv.org/abs/2506.08926, submitted (with Meike Hatzel, Kolja Knauer, Rose McCarty, and Torsten Ueckerdt)

28. Girth in GF(q)-representable matroids, https://arxiv.org/abs/2504.21797, Bulletin of the London Mathematical Society, to appear (with Meike Hatzel, Kolja Knauer, Rose McCarty, and Torsten Ueckerdt)

27. Preparing graph states forbidding a vertex-minor, https://arxiv.org/abs/2504.00291, submitted (with Andrew Jena)

26. Strongly sublinear separators and bounded asymptotic dimension for sphere intersection graphs, https://arxiv.org/abs/2504.00932, submitted (with Agelos Georgakopoulos, Meike Hatzel, and Rose McCarty)

25. Quasi-isometries between graphs with variable edge lengths, https://arxiv.org/abs/2503.07448, submitted (with Meike Hatzel, and Robert Hickingbotham)

24. Colouring t-perfect graphs, https://arxiv.org/abs/2412.17735, submitted  (with Maria Chudnovsky, Linda Cook, Sang-il Oum, and Jane Tan)

23. On high genus extensions of Negami's conjecture, https://arxiv.org/abs/2412.04420, submitted (with Marcin Briański, and Jane Tan)

22. Treewidth, Hadwiger number, and induced minors, https://arxiv.org/abs/2410.19295, submitted (with Rutger Campbell, Marc Distel, Bryce Frederickson, Pascal Gollin, Kevin Hendrey, Robert Hickingbotham, Sebastian Wiederrecht, David Wood, and Liana Yepremyan)

21. Counterexample to Babai's lonely colour conjecture, https://arxiv.org/abs/2410.05199, submitted (with Meike Hatzel, and Liana Yepremyan)

20. Polynomial Gyárfás-Sumner conjecture for graphs of bounded boxicity, https://arxiv.org/abs/2407.16882, submitted (with Yelena Yuditsky)

19. Fat minors cannot be thinned (by quasi-isometries), https://arxiv.org/abs/2405.09383, submitted (with Robert Hickingbotham, Freddie Illingworth, and Rose McCarty)

18. Geometric graphs with exponential chromatic number and arbitrary girth, https://arxiv.org/abs/2312.06898, The American Mathematical Monthly, to appear (with Matija Bucić)

17. Prime and polynomial distances in colourings of the plane, https://arxiv.org/abs/2308.02483, Israel Journal of Mathematics, to appear (with Rose McCarty, and Michał Pilipczuk)

16. A solution to Ringel's circle problem, https://arxiv.org/abs/2112.05042, Journal of the European Mathematical Society, to appear (with Chaya Keller, Linda Kleist, Shakhar Smorodinsky, and Bartosz Walczak)

Published

15. Reuniting χ-boundedness with polynomial χ-boundedness, https://arxiv.org/abs/2310.11167, Journal of Combinatorial Theory, Series B, 176:30--73, 2026 (with Maria Chudnovsky, Linda Cook, and Sang-il Oum)

14. Pivot-minors and the Erdős-Hajnal conjecture, https://arxiv.org/abs/2305.09133, Journal of Combinatorial Theory, Series B, 173:257--278, 2025

13. Chromatic number of spacetime, https://arxiv.org/abs/2308.16885, Acta Arithmetica, 218(1):65--76, 2025

12. On polynomial degree-boundedness, https://arxiv.org/abs/2311.03341, Advances in Combinatorics, 2024:5, 16pp (with Romain Bourneuf, Matija Bucić, and Linda Cook)

11. Odd distances in colourings of the plane, https://arxiv.org/abs/2209.15598, Geometric and Functional Analysis, 34(1):19--31, 2024

10. Separating polynomial χ-boundedness from χ-boundedness, https://arxiv.org/abs/2201.08814, Combinatorica, 44(1):1--8, 2024 (with Marcin Briański, and Bartosz Walczak)

9. Grounded L-graphs are polynomially χ-bounded, https://arxiv.org/abs/2108.05611, Discrete & Computational Geometry, 70(4):1523–1550, 2023 (with Tomasz Krawczyk, Rose McCarty, and Bartosz Walczak)

8. Triangle-free graphs with large chromatic number and no induced wheel, https://arxiv.org/abs/2104.05907, Journal of Graph Theory, 103(1):112--118, 2023

7. Colouring polygon visibility graphs and their generalizations, https://arxiv.org/abs/2103.07803, Journal of Combinatorial Theory, Series B, 161:268--300, 2023 (with Tomasz Krawczyk, Rose McCarty, and Bartosz Walczak)

6. Improved bounds for colouring circle graphs, https://arxiv.org/abs/2107.03585, Proceedings of the American Mathematical Society, 150(12):5121--5135, 2022

5. Vertex-minor-closed classes are χ-bounded, https://arxiv.org/abs/2008.05069, Combinatorica, 42(Suppl 1):1049--1079, 2022

4. Box and segment intersection graphs with large girth and chromatic number, https://arxiv.org/abs/2011.14174, Advances in Combinatorics, 2021:7, 9pp

3. Edge-maximal graphs on orientable and some nonorientable surfaces, https://arxiv.org/abs/1911.02666, Journal of Graph Theory, 98(3):405--425, 2021 (with Florian Pfender)

2. Circle graphs are quadratically χ-bounded, https://arxiv.org/abs/1905.11578, Bulletin of the London Mathematical Society, 53(3):673--679, 2021 (with Rose McCarty) 

1. Locally Hamiltonian graphs and minimal size of maximal graphs on a surface, https://arxiv.org/abs/2001.04836, The Electronic Journal of Combinatorics 27(2), (2020), #2.25 (with Carsten Thomassen)