A note on transformations of edge colorings of bipartite graphs

The author and A. Mirumian proved the following theorem: Let G be a bipartite graph with maximum degree Δ and let t , n be integers, t ⩾ n ⩾ Δ . Then it is possible to obtain, from one proper edge t-coloring of G, any proper edge n-coloring of G using only transformations of 2-colored and 3-colored subgraphs such that the intermediate colorings are also proper. In this note we show that if t > Δ then we can transform f to g using only transformations of 2-colored subgraphs. We also correct the algorithm suggested in [A.S. Asratian, Short solution of Kotzigʹs problem for bipartite graphs, J. Combin. Theory Ser. B 74 (1998) 160–168] for transformation of f to g in the case when t = n = Δ and G is regular.