James Davies
Currently I am a Junior Research Fellow at Trinity Hall, Cambridge. Before that, I did my PhD in Combinatorics and Optimization with Jim Geelen at the University of Waterloo between 2018 and 2022. I am interested in graph and matroid theory and their interactions with geometry. My email address is jgd37 at cam dot ac dot uk.
Publications
Submitted or Accepted
18. Explicit unit distance graphs with exponential chromatic number and arbitrary girth, https://arxiv.org/abs/2312.06898, submitted (with Matija Bucić)
17. On polynomial degree-boundedness, https://arxiv.org/abs/2311.03341, submitted (with Romain Bourneuf, Matija Bucić, and Linda Cook)
16. Reuniting χ-boundedness with polynomial χ-boundedness, https://arxiv.org/abs/2310.11167, submitted (with Maria Chudnovsky, Linda Cook, and Sang-il Oum)
15. Chromatic number of spacetime, https://arxiv.org/abs/2308.16885, submitted
14. Prime and polynomial distances in colourings of the plane, https://arxiv.org/abs/2308.02483, submitted (with Rose McCarty, and Michał Pilipczuk)
13. Pivot-minors and the Erdős-Hajnal conjecture, https://arxiv.org/abs/2305.09133, submitted
12. 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
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)