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On the edge colouring of bipartite graphs

Abstract For the bipartite graphs G(X, Y, E) such that the degrees of vertices y ∈ Y do not exceed q and the degrees of vertices x ∈ 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 ∈ X and the colours of edges incident with a vertex y ∈ Y coincide.