Some Results on the Classification for f - colored Graphs ∗
نویسندگان
چکیده
f -colorings have applications in scheduling problems. An f -coloring of a graph G is a coloring of edges of E(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 denoted by χ f (G). Any graph G has f -chromatic index equal to ∆ f (G) or ∆ f (G)+ 1, where ∆ f (G) = max v∈V {d d(v) f (v)e}. If χ ′ f (G) = ∆ f (G), then G is of C f 1; otherwise G is of C f 2. The f -core of G is the subgraph of G induced by the vertices of V ∗ 0 = {v : ∆ f (G) = d(v) f (v) ,v ∈V}. In this paper, some conditions for the classification on f -coloring are given.
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