Color critical hypergraphs with many edges

We show that for all k ≥ 3, r > l ≥ 2 there exists constant c = c(k, r, l) such that for large enough n there exists a k-color-critical r-uniform hypergraph on less than n vertices, having more than cnl edges, and having no l-set of vertices occuring in more than one edge. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 56–74, 2006