FACIAL R-ACYCLIC EDGE-COLORINGS OF PLANE GRAPHS
Kristína Budajová, Július Czap · International Journal of Pure and Apllied Mathematics · 2013
An edge-coloring of a 2-connected plane graph G is a facial r-acyclic edge-coloring if every facial cycle C in G is colored with at least min{|C|, r} colors, in addition, no two face-adjacent edges (consecutive edges of a facial trail of some face) receive the same color.The minimum number of colors used in such a coloring of G is denoted by a ′ f r (G).In this paper, we determine tight upper bounds for a ′ f r (G).