127 Equitable Edge-Colorings of (k(f−1)+1,kf)-Graph and (k(f−1 ),kf−1)-Graph Available to Purchase

An edge-coloring of a graph G is equitable if, for each v ∈ V(G), the number of edges colored with any one color incident with v differs form the number of edges colored with any other color incident with v by at most one. By study the factorization, we prove that 1) every (k(f−1)+1,kf)-graph has equitable edge-coloring with k colors; 2) for any subgraph H with r edges of (k(f−1 ),kf −1)-graph G, there exist a subgraph R with an equitable edge-coloring orthogonal to H.