An edge coloring of a graph 
assigns colors to its edges
such that any two edges incident on the same graph
vertex receive different colors. An edge coloring containing the smallest possible
number of colors for a given graph is known as a minimum
edge coloring. Finding a minimum edge coloring
is the edge coloring problem.
The edge chromatic number gives the minimum number of colors with which a graph's edges
can be colored.
A D-coloring is a proper edge coloring that additionally makes every diamond graph subgraph a rainbow
subgraph (Verma 2026).
A B-coloring instead requires every cycle graph 
to be a rainbow subgraph, in addition to properness
(Martin et al. 2026).
See also
Chromatic Number,
Colorful Cycle,
Coloring,
Edge
Chromatic Number,
Edge Coloring Problem,
Graph Coloring,
k-Coloring,
Labeled Graph,
Minimum
Edge Coloring,
Minimum Vertex Coloring,
Proper Coloring,
Vertex
Coloring
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References
Fiorini, S. and Wilson, R. Edge-Colourings of Graphs. Pittman, 1977.Martin, R. R.; Ruszinkó,
M.; and Sárközy, G. N. "Bounds for B-Coloring Planar and Outerplanar
Graphs." 27 Oct 2026. https://arxiv.org/abs/2610.37497.Saaty,
T. L. and Kainen, P. C. The
Four-Color Problem: Assaults and Conquest. New York: Dover, p. 13, 1986.Verma,
H. "A Proof of Wang's Planar D-Coloring Conjecture." 23 Oct 2026. https://arxiv.org/abs/2610.33322.Referenced
on Wolfram|Alpha
Edge Coloring
Cite this as:
Weisstein, Eric W. "Edge Coloring." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EdgeColoring.html
Subject classifications
