On the Choice Number of Random Hypergraphs

Authors:
Van H. Vu
Affiliations:
Microsoft Research, Microsoft Corp., Redmond, WA 98052, USA (e-mail: vanhavu@microsoft.com)
Venue:
Combinatorics, Probability and Computing
Year:
2000

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Abstract

We generalize the notion of choice number from graphs to hypergraphs and estimate the sharp order of magnitude of the choice number of random hypergraphs. It turns out that the choice number and the chromatic number of a random hypergraph have the same order of magnitude, almost surely. Our result implies an earlier bound on the chromatic number of random hypergraphs, proved by Schmidt [23] using a different method.