Geodesic
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. 
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     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/}
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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/