| Title: |
Extending the Continuum of Six-Colorings |
| Authors: |
Mundinger, Konrad, Pokutta, Sebastian, Spiegel, Christoph, Zimmer, Max |
| Publication Year: |
2024 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Combinatorics |
| More Details: |
We present two novel six-colorings of the Euclidean plane that avoid monochromatic pairs of points at unit distance in five colors and monochromatic pairs at another specified distance $d$ in the sixth color. Such colorings have previously been known to exist for $0.41 < \sqrt{2} - 1 \le d \le 1 / \sqrt{5} < 0.45$. Our results significantly expand that range to $0.354 \le d \le 0.657$, the first improvement in 30 years. Notably, the constructions underlying this were derived by formalizing colorings suggested by a custom machine learning approach.
Comment: An animated version of Figure 2 is available at https://christophspiegel.berlin/hn/fig2.pdf and can be viewed with Acrobat Reader |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2404.05509 |
| Accession Number: |
edsarx.2404.05509 |
| Database: |
arXiv |
