Judicious bisection of hypergraphs

Judicious bisection of hypergraphs asks for a balanced bipartition of the vertex set that optimizes several quantities simultaneously. In this paper, we prove that if G is a hypergraph with n vertices and m i edges of size i for i = 1, 2, ., k, then G admits a bisection in which each vertex class spans at most m12+14m2+.+(12k)mk+o(m1+.+mk) edges, where G is dense enough or .(G) = o(n) but has no isolated vertex, which turns out to be a bisection version of a conjecture proposed by Bollobás and Scott.