Judicious partitions of uniform hypergraphs

The vertices of any graph with m edges may be partitioned into two parts so that each part meets at least edges. Bollobas and Thomason conjectured that the vertices of any r-uniform hypergraph with m edges may likewise be partitioned into r classes such that each part meets at least edges. In this paper we prove the weaker statement that, for each r a parts per thousand yen 4, a partition into r classes may be found in which each class meets at least edges, a substantial improvement on previous bounds.