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The vertices of any graph with m edges may be partitioned into two parts so that each part meets at least $$\tfrac{{2m}} {3}$$ 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 $$\tfrac{r} {{2r - 1}}$$ edges. In this paper we prove the weaker statement that, for...
The vertices of any graph with m edges can 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 graph may be likewise partitioned into r classes such that each part meets at least cm edges, with $$\frac{r} {{2r - 1}}$$ . In this paper, we prove this conjecture for the case r=3. In the...
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