Hypergraphs of special type and CUT polytope relaxations properties analysis

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.