Geodesic
On a family of 0/1-polytopes with an NP-complete criterion for vertex nonadjacency relation
Diskretnaya Matematika, Tome 29 (2017) no. 2, pp. 29-39.

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In 1995 T. Matsui considered a special family of 0/1-polytopes with an NP-complete criterion for vertex nonadjacency relation. In 2012 the author demonstrated that all polytopes of this family appear as faces of polytopes associated with the following NP-complete problems: the travelling salesman problem, the 3-satisfiability problem, the knapsack problem, the set covering problem, the partial ordering problem, the cube subgraph problem, and some others. Here it is shown that none of the polytopes of the aforementioned special family (with the exception of the one-dimensional segment) can appear as a face in a polytope associated with the problem of the maximum independent set, the set packing problem, the set partitioning problem, and the problem of 3-assignments.
Keywords: affine reduction, set covering, set partitioning. 
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A. N. Maksimenko. On a family of 0/1-polytopes with an NP-complete criterion for vertex nonadjacency relation. Diskretnaya Matematika, Tome 29 (2017) no. 2, pp. 29-39. http://geodesic.mathdoc.fr/item/DM_2017_29_2_a2/

[1] Michael R. G., Johnson D. S., Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, 1979, 338 pp. | MR | MR | Zbl

[2] Emelichev V. A., Kovalev M. M., Kravtsov M. K., Mnogogranniki, grafy, optimizatsiya, Nauka, M., 1981, 346 pp. | MR

[3] Maksimenko A. N., “On affine reducibility of combinatorial polytopes”, Doklady Mathematics, 85:2 (2012), 283–285 | DOI | MR | Zbl

[4] Maksimenko A. N., “The common face of some 0/1-polytopes with NP-complete nonadjacency relation”, J. Math. Sci., 203:6 (2014), 823–832 | DOI | MR | Zbl

[5] Balas E., Saltzman M. J., “Facets of the three-index assignment polytope”, Discrete Applied Mathematics, 23:3 (1989), 201–229 | DOI | MR | Zbl

[6] Chvátal V., “On certain polytopes associated with graphs”, J. Comb.Theory, Ser. B, 18:2 (1975), 138–154 | DOI | MR | Zbl

[7] Ikura Y., Nemhauser G. L., “Simplex pivots on the set packing polytope”, Math. progr., 33:2 (1985), 123–138 | DOI | MR | Zbl

[8] Maksimenko A. N., “A special role of Boolean quadratic polytopes among other combinatorial polytopes”, Modelir. i analiz inf. sistem, 23:1 (2016), 23–40 | MR

[9] Matsui T., “NP-completeness of non-adjacency relations on some 0-1-polytopes”, Lect. Notes Oper. Res., 1 (1995), 249–258