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{\bf Alan Frieze and Dhruv Mubayi}
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{\bf On the Chromatic Number of Simple Triangle-Free Triple Systems}
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A hypergraph is simple if every two edges share at most one vertex.
It is triangle-free if in addition every three pairwise intersecting
edges have a vertex in common. We prove that there is an absolute
constant $c$ such that the chromatic number of a simple triangle-free
triple system with maximum degree $\Delta$ is at most
$c\sqrt{\Delta/\log \Delta}$.  This extends a result of Johansson
about graphs, and is sharp apart from the constant $c$.



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