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arXiv · 1701.05855

Judicious partitions of uniform hypergraphs

John Haslegrave
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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.

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John Haslegrave. 2017-01-20. Judicious partitions of uniform hypergraphs. https://doi.org/10.1007/s00493-014-2916-7

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