The List-Chromatic Number of Complete Multipartite Hypergraphs and Multiple Covers by Independent Sets
Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 454-465
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This paper deals with list colorings of uniform hypergraphs. Let $H(m,r,k)$ be the complete $r$-partite $k$-uniform hypergraph with parts of equal size $m$ in which each edge contains exactly one vertex from some $k\le r$ parts. Using results on multiple covers by independent sets, we establish that, for fixed $k$ and $r$, the list-chromatic number of $H(m,r,k)$ is $(1+o(1))\log_{r/(r-k+1)}(m)$ as $m\to\infty$.
Keywords:
hypergraphs, independent sets, list colorings, multiple covers.
@article{MZM_2020_107_3_a10,
author = {D. A. Shabanov and T. M. Shaikheeva},
title = {The {List-Chromatic} {Number} of {Complete} {Multipartite} {Hypergraphs} and {Multiple} {Covers} by {Independent} {Sets}},
journal = {Matemati\v{c}eskie zametki},
pages = {454--465},
publisher = {mathdoc},
volume = {107},
number = {3},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a10/}
}
TY - JOUR AU - D. A. Shabanov AU - T. M. Shaikheeva TI - The List-Chromatic Number of Complete Multipartite Hypergraphs and Multiple Covers by Independent Sets JO - Matematičeskie zametki PY - 2020 SP - 454 EP - 465 VL - 107 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a10/ LA - ru ID - MZM_2020_107_3_a10 ER -
%0 Journal Article %A D. A. Shabanov %A T. M. Shaikheeva %T The List-Chromatic Number of Complete Multipartite Hypergraphs and Multiple Covers by Independent Sets %J Matematičeskie zametki %D 2020 %P 454-465 %V 107 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a10/ %G ru %F MZM_2020_107_3_a10
D. A. Shabanov; T. M. Shaikheeva. The List-Chromatic Number of Complete Multipartite Hypergraphs and Multiple Covers by Independent Sets. Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 454-465. http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a10/