This is the sixteenth “research” thread of the Polymath16 project to make progress on the Hadwiger–Nelson problem, continuing this post. This project is a follow-up to Aubrey de Grey’s breakthrough result that the chromatic number of the plane is at least 5. Discussion of the project of a non-research nature should continue in the Polymath proposal page. We will summarize progress on the Polymath wiki page.
The paper writing has found a second wind between Philip Gibbs, Aubrey de Grey, Jaan Parts and Tom Sirgedas. For reference, I wanted to compile a list of related publications that have emerged since starting our project. (Feel free to any references I missed in the comments.) There has certainly been a bit of activity since Aubrey’s paper first hit the arXiv two years ago!
P. Ágoston, Probabilistic formulation of the Hadwiger–Nelson problem.
F. Bock, Epsilon-colorings of strips, Acta Math. Univ. Comenianae (2019) 88: 469-473.
G. Exoo, D. Ismailescu, A 6-chromatic two-distance graph in the plane, arXiv preprint arXiv:1909.13177 (2019).
G. Exoo, D. Ismailescu, The chromatic number of the plane is at least 5: A new proof, Discrete & Computational Geometry (2019): 1-11.
G. Exoo, D. Ismailescu, The Hadwiger-Nelson problem with two forbidden distances, arXiv preprint arXiv:1805.06055 (2018).
N. Frankl, T. Hubai, D. Pálvölgyi, Almost-monochromatic sets and the chromatic number of the plane, arXiv preprint arXiv:1912.02604 (2019).
M. J. H. Heule, Computing a Smaller Unit-Distance Graph with Chromatic Number 5 via Proof Trimming, arXiv preprint arXiv:1907.00929 (2019).
M. J. H. Heule, Searching for a Unit-Distance Graph with Chromatic Number 6, SAT COMPETITION 2018: 66.
M. J. H. Heule, Trimming Graphs Using Clausal Proof Optimization, In International Conference on Principles and Practice of Constraint Programming, pp. 251-267. Springer, Cham, 2019.
J. Parts. A small 6-chromatic two-distance graph in the plane, Geombinatorics, vol. 29, No. 3 (2020), pp.111-115.
J. Parts. Graph minimization, focusing on the example of 5-chromatic unit-distance graphs in the plane, Geombinatorics, vol. 29, No. 4 (2020), pp.137-166.