Short Solution of Kotzigʹs Problem for Bipartite Graphs

In 1975, A. Kotzig posed the following problem: LetGbe at-regular graph which has a proper edget-coloring,t⩾4. Is it possible to obtain, from one proper edget-coloring ofG, any other proper edge t-coloring of G using only transformations of 2-colored and 3-colored subgraphs such that the intermediate colorings are also proper? The author and A. N. Mirumian proved that it is possible ifGis a bipartite graph. We give here a short proof of this result.