On the cromatic number of infinitesimal plane layer

Abstract

We consider natural generalization of plane chromatic number problem. We consider chromatic numbers $\chi$ of spaces ${\mathbb{R}}^n\times [0,\epsilon {]}^k$ for arbitrary small $\epsilon$. We prove that $5\le \chi ({\mathbb{R}}^2\times [0,\epsilon ])\le 7$ and $6\le \chi ({\mathbb{R}}^2\times [0,\epsilon {]}^2)\le 7$. Also we consider natural questions, arising from this considerations.

13 pages, 3 figures, in Russian

References in corpus (2)

• Fractional and $j$-fold colouring of the plane
• Chromatic properties of the Euclidean plane