This is the thirteenth “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.
Interest in this project has spiked since approaching (and passing) our original deadline of April 15. For this reason, I propose we extend the deadline to October 15, 2019. We can discuss this in the Polymath proposal page.
Here are some recent developments:
- The fractional chromatic number of the plane is at least 3.98.
- The smallest known 5-chromatic unit distance graph has 529 vertices and 2630 edges.
- Dömötör has an exciting idea for finding a human-verifiable proof that the chromatic number of the plane is at least 5.
I’m interested to see if this last point has legs!