Geodesic
On interval edge $\Delta$-colouring
Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 94-95

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It is shown that there is a $(6,3)$-biregular graph $G=(X,Y,E)$, such that $|X|+|Y|=33$, with no interval $6$-colourings, and it is proved that the $\Delta$-colouring problem for bipartite multigraph $G=(X,Y,E)$ is $NP$-complete even if $|X|=2$. 
@article{PDMA_2012_5_a48,
     author = {A. M. Magomedov},
     title = {On interval edge $\Delta$-colouring},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {94--95},
     publisher = {mathdoc},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2012_5_a48/}
}
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A. M. Magomedov. On interval edge $\Delta$-colouring. Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 94-95. http://geodesic.mathdoc.fr/item/PDMA_2012_5_a48/