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

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 $|X|=2$. 
@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/}
}
TY  - JOUR
AU  - A. M. Magomedov
TI  - On interval edge $\Delta$-colouring
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2012
SP  - 94
EP  - 95
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2012_5_a48/
LA  - ru
ID  - PDMA_2012_5_a48
ER  - 
%0 Journal Article
%A A. M. Magomedov
%T On interval edge $\Delta$-colouring
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2012
%P 94-95
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2012_5_a48/
%G ru
%F PDMA_2012_5_a48
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/

[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