# Judicious partitions of 3-uniform hypergraphs

John Haslegrave

Arxiv ID: 0911.0563•Last updated: 8/12/2020

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. Bollob\'as 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 $c=\frac{r}{2r-1}$. In this paper, we prove this conjecture for the case
$r=3$. In the course of the proof we shall also prove an extension of the graph
case which was conjectured by Bollob\'as and Scott.

#### PaperStudio AI Chat

I'm your research assistant! Ask me anything about this paper.