Continued Fractions and the Four Color Theorem
Year: 2025
Type: article
Abstract: We study the geometry of some proper 4-colorings of the vertices of sphere triangulations with degree sequence 6,...,6,2,2,2. Such triangulations are the simplest examples which have non-negative combinatorial curvature. The examples we construct, which are roughly extremal in some sense, are based on a novel geometric interpretation of continued fractions. We will also present a conjectural sharp “isoperimetric inequality” for colorings of this kind of triangulation.
Author: Richard Schwartz
Institution: Brown University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4408045199