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- W2607522182 abstract "Let χ l ( G ) denote the list chromatic number of the r ‐uniform hypergraph G . Extending a result of Alon for graphs, Saxton and the second author used the method of containers to prove that, if G is simple and d ‐regular, then . To see how close this inequality is to best possible, we examine χ l ( G ) when G is a random r ‐partite hypergraph with n vertices in each class. The value when r = 2 was determined by Alon and Krivelevich; here we show that almost surely, where d is the expected average degree of G and . The function g ( r , α ) is defined in terms of “preference orders” and can be determined fairly explicitly. This is enough to show that the container method gives an optimal lower bound on χ l ( G ) for r = 2 and r = 3, but, perhaps surprisingly, apparently not for r ≥ 4." @default.
- W2607522182 created "2017-05-05" @default.
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- W2607522182 date "2019-04-01" @default.
- W2607522182 modified "2023-09-24" @default.
- W2607522182 title "List colorings of multipartite hypergraphs" @default.
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- W2607522182 doi "https://doi.org/10.1002/rsa.20848" @default.
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