Geodesic
On the edge colouring of bipartite graphs
Diskretnaya Matematika, Tome 21 (2009) no. 2, pp. 153-158.

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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. 
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A. M. Magomedov. On the edge colouring of bipartite graphs. Diskretnaya Matematika, Tome 21 (2009) no. 2, pp. 153-158. http://geodesic.mathdoc.fr/item/DM_2009_21_2_a11/

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[2] Svami M., Tkhulasiraman K., Grafy, seti i algoritmy, Mir, Moskva, 1984