On a list $(k,l)$-coloring of incidentors in multigraphs of even degree for some values of $k$ and $l$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 2, pp. 177-184
Voir la notice de l'article provenant de la source Math-Net.Ru
The problem of a list $(k,l)$-coloring of incidentors of a directed multigraph without loops is studied in the case where the lists of admissible colors for incidentors of each arc are integer intervals. According to a known conjecture, if the lengths of these interval are at least $2\Delta+2k-l-1$ for every arc, where $\Delta$ is the maximum degree of the multigraph, then there exists a list $(k,l)$-coloring of incidentors. We prove this conjecture for multigraphs of even maximum degree $\Delta$ with the following parameters:
$\bullet \ l\ge k+\Delta/2$;
$\bullet \ l k+\Delta/2$ and $k$ or $l$ is odd;
$\bullet \ l k+\Delta/2$ and $k=0$ or $l-k=2$.
Keywords:
list coloring, incidentors, $(k,l)$-coloring.
@article{TIMM_2019_25_2_a16,
author = {A. V. Pyatkin},
title = {On a list $(k,l)$-coloring of incidentors in multigraphs of even degree for some values of $k$ and $l$},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {177--184},
publisher = {mathdoc},
volume = {25},
number = {2},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2019_25_2_a16/}
}
TY - JOUR AU - A. V. Pyatkin TI - On a list $(k,l)$-coloring of incidentors in multigraphs of even degree for some values of $k$ and $l$ JO - Trudy Instituta matematiki i mehaniki PY - 2019 SP - 177 EP - 184 VL - 25 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2019_25_2_a16/ LA - ru ID - TIMM_2019_25_2_a16 ER -
%0 Journal Article %A A. V. Pyatkin %T On a list $(k,l)$-coloring of incidentors in multigraphs of even degree for some values of $k$ and $l$ %J Trudy Instituta matematiki i mehaniki %D 2019 %P 177-184 %V 25 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2019_25_2_a16/ %G ru %F TIMM_2019_25_2_a16
A. V. Pyatkin. On a list $(k,l)$-coloring of incidentors in multigraphs of even degree for some values of $k$ and $l$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 2, pp. 177-184. http://geodesic.mathdoc.fr/item/TIMM_2019_25_2_a16/