Geodesic
On interval edge $\Delta$-colouring
Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 94-95 
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/
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     author = {A. M. Magomedov},
     title = {On interval edge $\Delta$-colouring},
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     year = {2012},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2012_5_a48/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $|X|=2$.

[1] Asratyan A. S., Kamalyan R. R., “Intervalnye raskraski rëber multigrafa”, Prikladnaya matematika, 5, Izd-vo Erevan. un-ta, Erevan, 1987, 25–34 | MR

[2] Sevastyanov S. V., “Ob intervalnoi raskrashivaemosti rëber dvudolnogo grafa”, Metody diskretnogo analiza, 50, 1990, 61–72 | MR

[3] Asratian A. S., Casselgren C. J., Some results on interval edge colorings of ($\alpha,\beta$)-biregular bipartite graphs, Linköpingsuniversitet, Linköping, Sweden, 2006