Abstract
The first author showed that the list chromatic number of every graph with average degree d is at least (0.5−o(1))log2d. We prove that for r≥3, every r-uniform hypergraph in which at least half of the (r−1)-vertex subsets are contained in at least d edges has list chromatic number at least lnd100r3. When r is fixed, this is sharp up to a constant factor.
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