Geodesic
A paintability version of the combinatorial Nullstellensatz, and list colorings of \(k\)-partite \(k\)-uniform hypergraphs
The electronic journal of combinatorics, Tome 17 (2010)
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We study the list coloring number of $k$-uniform $k$-partite hypergraphs. Answering a question of Ramamurthi and West, we present a new upper bound which generalizes Alon and Tarsi's bound for bipartite graphs, the case $k=2$. Our results hold even for paintability (on" line list colorability). To prove this additional strengthening, we provide a new subject"=specific version of the Combinatorial Nullstellensatz.
DOI : 10.37236/448
Classification : 05C15, 11C08, 91A43, 05C65, 05C50
Mots-clés : list coloring number, combinatorial nullstellensatz 
@article{10_37236_448,
     author = {Uwe Schauz},
     title = {A paintability version of the combinatorial {Nullstellensatz,} and list colorings of \(k\)-partite \(k\)-uniform hypergraphs},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/448},
     zbl = {1201.05039},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/448/}
}
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Uwe Schauz. A paintability version of the combinatorial Nullstellensatz, and list colorings of \(k\)-partite \(k\)-uniform hypergraphs. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/448

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