Hypergraph cuts above the average

  title={Hypergraph cuts above the average},
  author={D. Conlon and J. Fox and Matthew Kwan and B. Sudakov},
  journal={arXiv: Combinatorics},
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. That is, there exist cuts which exceed the expected size of a random cut by some multiple of the standard deviation. We study analogues of this and related results in hypergraphs. First, we observe… Expand

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