论文标题
通过翻译圆圈的彩色图
Coloring graphs by translates in the circle
论文作者
论文摘要
分数和圆形色数是图形的色数的两个最多研究的非整合细化。从图形的着色底座的定义开始，该图的起源于与厄尔贡理论相关的工作，我们正式化了图形的陀螺仪的概念：顶点是通过圆圈组中的单个鲍尔集的翻译来彩色的，而相邻的顶点则接收了不相交的转换。图形的相应旋律数始终位于分数色数和圆形色素数之间。我们研究了陀螺分校的基本特性。特别是，我们构造了术示例的示例，其旋律数严格介于分数色数和圆形色数之间。我们还建立了几个等效定义的旋律数字，包括涉及所有有限阿贝尔组的版本。
The fractional and circular chromatic numbers are the two most studied non-integral refinements of the chromatic number of a graph. Starting from the definition of a coloring base of a graph, which originated in work related to ergodic theory, we formalize the notion of a gyrocoloring of a graph: the vertices are colored by translates of a single Borel set in the circle group, and neighbouring vertices receive disjoint translates. The corresponding gyrochromatic number of a graph always lies between the fractional chromatic number and the circular chromatic number. We investigate basic properties of gyrocolorings. In particular, we construct examples of graphs whose gyrochromatic number is strictly between the fractional chromatic number and the circular chromatic number. We also establish several equivalent definitions of the gyrochromatic number, including a version involving all finite abelian groups.
