Given a graph G and a subgraph H of G, let rb(G,H) be the minimum number r for which any edge-coloring of G with r colors has a rainbow subgraph H. The number rb(G,H) is called the rainbow number of H with respect to G. Denote mK2 a matching of size m and Bn,k a k-regular bipartite graph with bipartition (X,Y ) such that |X| = |Y | = n and k ≤ n. In this… (More)