Continued Fractions and the 4-Color Theorem [article]

Richard Evan Schwartz
2023 arXiv   pre-print
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 also present a conjectural sharp "isoperimetric inequality" for colorings of this kind of triangulation.
arXiv:2208.05254v6 fatcat:genofrqkf5h2bg6oyepu7okc4a