Geodesic
Hypergraphs of special type and CUT polytope relaxations properties analysis
Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 3, pp. 82-100

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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.
Keywords: hypergraphs, cut polytope relaxations, rooted semimetric polytope, integrity recognition. 
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     author = {A. V. Nikolaev},
     title = {Hypergraphs of special type and {CUT} polytope relaxations properties analysis},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {82--100},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2011_18_3_a8/}
}
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A. V. Nikolaev. Hypergraphs of special type and CUT polytope relaxations properties analysis. Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 3, pp. 82-100. http://geodesic.mathdoc.fr/item/MAIS_2011_18_3_a8/