Coloring graphs by translates in the circle

The fractional and circular chromatic numbers are the two most studied non-integral refinements of number a graph. Starting from definition coloring base graph, which originated in work related to ergodic theory, we formalize notion gyrocoloring graph: vertices colored by translates single Borel set circle group, neighboring receive disjoint translates. corresponding gyrochromatic graph always lies between number. We investigate basic properties gyrocolorings. In particular, construct examples graphs whose is strictly also establish several equivalent definitions number, including version involving all finite abelian groups.