论文标题
持续的分数和4色定理
Continued Fractions and the 4-Color Theorem
论文作者
论文摘要
我们研究了具有度序列6，...，6,2,2,2的球体顶点的一些适当4色的几何形状。这样的三角剖分是具有非负组合曲率的最简单示例。我们构建的示例在某种意义上大致是极端的，是基于对持续分数的新几何解释。我们还为这种三角剖分的着色提出了一种猜想的尖锐的“等值不平等”。
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.
