On the Chromatic Number of Simple Triangle-Free Triple Systems

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 Δ is at most c√Δ/log Δ. This extends a result of Johansson about graphs, and is sharp apart from the constant c.