SOME GRAPHS IN $C_f2$ BASED ON $f$-COLORING

Let G = (V, E) be a graph and f : V → Z + a positive integer be a function.An f-coloring of G is a coloring of the edges such that every vertex v ∈ V is incident to at most f (v) edges of the same color.The minimum number of colors of anIn this paper, we give some sufficient conditions for a graph to be in C f 2. One of the results is a generalization of a theorem by Zhang et al. (2008).Moreover, we show that, when f is constant and a divisor of (n -1), a maximal subgraph of the complete graph K n which is in class C f 1 has precisely n 2 -∆ f (K n )/2 edges.