A D-coloring of a simple graph is a proper edge coloring in which every subgraph isomorphic to the diamond graph is a rainbow subgraph. Thus the five edges of each such diamond receive five different colors (Wang 2026).
Verma (2026) proved that every planar graph of maximum vertex degree 
has a D-coloring using at most 
colors, completing Wang's conjecture. The case 
uses computer-assisted verification
of reducible configurations.
A B-coloring, which requires every cycle graph 
to be rainbow in addition to properness, is a stronger condition. The outer 
of a diamond
graph uses four distinct colors, and its remaining graph
edge must receive a fifth. Conversely, a two-color edge
coloring of 
is a D-coloring but not a B-coloring.
