The recent breakthrough work by de Grey that showed the chromatic number of the plane could not be equal to 4 (and so must be 5, 6 or 7) has been published, along with a few other papers in a special issue of the journal Geombinatorics. There are free copies of all the articles in this subscription journal around the place, so I thought I’d gather links to all of them here.
- Breakthrough in My Favorite Open Problem of Mathematics: Chromatic Number of the Plane, Alexander Soifer (this is a shorter version of the full published article, which has a slightly different title: Progress in My Favorite Open Problem of Mathematics, Chromatic Number of the Plane: An Étude in Five Movements)
Computing Small Unit-Distance Graphs with Chromatic Number 5, Marijn J.H. Heule (arXiv:1805.12181)
The Hadwiger-Nelson problem with two forbidden distances, Geoffrey Exoo, Dan Ismailescu (arXiv:1805.06055)
Apparently, Exoo and Ismailescu managed to rule out the case that the chromatic number is 4 independently and at about the same time as de Grey, but wanted to improve the construction and shrink the graph they used, and so were scooped while they kept working in secret.