Title: Judicious partitions of uniform hypergraphs,
Abstract: The vertices of any graph with $m$ edges may be partitioned into two parts so
that each part meets at least $\frac{2m}{3}$ edges. Bollobás 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
$\frac{r}{2r-1}m$ edges. In this paper we prove the weaker statement that, for
each $r\ge 4$, a partition into $r$ classes may be found in which each class
meets at least $\frac{r}{3r-4}m$ edges, a substantial improvement on previous
bounds.