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Continued Fractions and the 4-Color Theorem - MaRDI portal

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Continued Fractions and the 4-Color Theorem

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Publication:6506397

arXiv2208.05254MaRDI QIDQ6506397

Author name not available (Why is that?)


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.












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