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Continued Fractions and the 4-Color Theorem
- Publication Year :
- 2022
-
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 also present a conjectural sharp "isoperimetric inequality" for colorings of this kind of triangulation.<br />Comment: This version is the same as the previous one, except that I edited it to remove typos and other little glitches
- Subjects :
- Mathematics - Combinatorics
Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2208.05254
- Document Type :
- Working Paper