The edge chromatic number e (G) of a graph G is the minimum number of colors

The edge chromatic number Χ_e(G) of a graph G is the minimum number of colors needed for coloring the edges of G so that incident edges get different colors. Clearly, Χ_e(G) ≥ max d(u), where d(u) is the degree of vertex u. If G = (S, T; E) is bipartite, the equality sign holds. Prove this for K_n,n the complete bipartite graph G = (S, T, E) with S and T consisting of n vertices each.