Coloring edges of graphs embedded in a surface of characteristic zero

Consider graphs that are embeddable in a surface of characteristic zero. Class two graphs of this type with maximum degree Δ⩽6 are known to exist. Hind and Zhao showed that such graphs with maximum degree Δ⩾8 must be class one. This article shows that such graphs with maximum degree Δ=7 also must be class one, completing the analysis of these surfaces. These are the first surfaces where the maximum degree of class two graphs has been determined.