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 neighboring 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.

分数色数和圆形色数是对图的色数进行的研究最多的两个非整数改进。从图的着色基础的定义开始，该定义起源于与遍历理论相关的工作，我们将图的陀螺着色的概念形式化：顶点通过在圆组中的单个Borel集的平移进行着色，并且相邻顶点接收不相交的平移。图的相应回旋色数始终位于分数色数和圆形色数之间。我们研究了陀螺色的基本特性。特别是，我们构造了回旋色数严格在分数色数和圆色数之间的图的示例。我们还为陀螺色数建立了几个等效的定义，