Georgia Institute of Technology College of Sciences

An $r$-cut of a $k$-uniform hypergraph $H$ is a partition of the vertex set of $H$ into $r$ parts and the size of the cut is the number of edges which have a vertex in each part. A classical result of Edwards says that every $m$-edge graph has a 2-cut of size $m/2+\Omega(\sqrt{m})$, and this is best possible. In this talk we will discuss recent results on analogues of Edwards’ result and related problems in hypergraphs.