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An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v ∈ V(G) at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index of G and is denoted by x′f(G). Any simple graph G has the f-chromatic index equal to Δf(G) or Δf(G) + 1, where Δf(G) = maxv∈V(G){⌈d(v)/f(v)⌊}. If x′f(G) = Δf(G), then G is of f-class...
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