Judicious partitions of 3-uniform hypergraphs

John Haslegrave
Arxiv ID: 0911.0563Last 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.

Related papers

Commercial Disclosure
© 2023 Paper Studio™. All Rights Reserved.