Hypergraphs of Special Type and CUT Polytope Relaxations Properties Analysis

Abstract

The topic of the research is a relationship between a class of hypergraphs of a special
type and properties of the points of the cut polytope relaxations $M_{n,k}$. It is established
that for a sufficiently large $n$ in $M_{n,4}$ and $M_{n,5}$ polytopes, there are points which have
no integer vertices in any expansion in a convex combination of $M_{n,3}$ vertices.