SMALLEST n-UNIFORM HYPERGRAPH WITH POSITIVE DISCREPANCY
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چکیده
A two-coloring of the vertices X of the hypergraph H = ( X , o °) by red and blue has discrepancy d if d is the largest difference between the number of red and blue points in any edge. A two-coloring is an equipartition of H if it has discrepancy 0, i.e., every edge is exactly half red and half blue. Letf(n) be the fewest number of edges in an n-uniform hypergraph (all edges have size n) having positive discrepancy. Erd6s and S6s asked: is f(n) unbounded? We answer this question in the affirmative and show that there exist constants cl and c2 such that
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تاریخ انتشار 1987