3 papers
math.CO2026
The chromatic number of is at least 25
Jaan Parts
The lower bound for the chromatic number of the Euclidean space of dimension 8 is increased to 25.
math.CO2020
What percent of the plane can be properly 5- and 6-colored?
Jaan Parts
We present a tiling of more than 99.985698% of the Euclidean plane with six colors, reducing the previous record for uncovered fraction of the plane by about 12.8%. We also present…
math.CO2020
The chromatic number of the plane is at least 5 -- a human-verifiable proof
Jaan Parts
We present a new proof of the known fact that the chromatic number of the plane is at least 5. The main difference of this proof is that it can be verified manually without the hel…