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A hypergraph  H  = ( V ,  E ) has the property  B k   if there exists an assignment of two colors to  V  such that each edge contains at least  k  vertices of each color. A hypergraph is called simple if every two edges of it have at most one common vertex. We obtain a new lower bound for the minimal number of edges of  n -uniform simple hypergraph without the property  B k  .

New lower bound for the minimal number of edges of simple uniform hypergraph without the property B k