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For k-uniform hypergraphs F and H and an integer r 2, let cr;F (H) denote the number of r-colorings of the set of hyperedges of H with no monochromatic copy of F and let cr;F (n) = maxH2Hn cr;F (H), where the maximum runs over the familyHn of all k-uniform hypergraphs on n vertices. Moreover, let ex(n;F ) be the usual Tur an function , i.e., the maximum number of hyperedges of an n-vertex k-uniform hypergraph which contains no copy of F . In this paper, we consider the question for determining cr;F (n) for arbitrary xed hypergraphs F and show

A structural result for hypergraphs with many restricted edge colorings