Cyclic colorings of plane graphs with independent faces
  Let G be a plane graph with maximum face size D. If all faces of G with size four or more are vertex disjoint, then G has a cyclic coloring with D+1 colors, i.e., a coloring such that all vertices incident with the same face receive distinct colors. 
Jernej Azarija, Daniel Kr\'al', Rok Erman, Matjaz Krnc, Ladislav   Stacho