On the edge colouring of bipartite graphs

For the bipartite graphs $G(X,Y,E)$ such that the degrees of vertices $y\in Y$ do not exceed $q$ and the degrees of vertices $x\in X$ are equal to $2q$, we consider the problem of existence of the edge 2-colouring such that $q$ edges of each colour are incident with each vertex $x\in X$ and the colours of edges incident with a vertex $y\in Y$ coincide.