Improved Bounds for Uniform Hypergraphs without Property B
  A hypergraph is said to be properly 2-colorable if there exists a 2-coloring of its vertices such that no hyperedge is monochromatic. On the other hand, a hypergraph is called non-2-colorable if there exists at least one monochromatic hyperedge in each of the possible 2-colorings of its vertex set. Let m(n) denote the minimum number of hyperedges in a non-2-colorable n-uniform hypergraph. Establishing the lower and upper bounds on m(n) is a well-studied research direction over several decades. In this paper, we present new constructions for non-2-colorable n-uniform hypergraphs. These constructions improve the upper bounds for m(8), m(13), m(14), m(16) and m(17). We also improve the lower bound for m(5). 
Sachin Aglave and V. A. Amarnath and Saswata Shannigrahi and Shwetank   Singh
math.CO