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Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 8, Pages 34–42 (Mi ivm8729)  

This article is cited in 4 scientific papers (total in 4 papers)

An analog of the Cook theorem for polytopes

A. N. Maksimenko

Chair of Discrete Analysis, Yaroslavl State University, Yaroslavl, Russia

Abstract: We prove that the polytope $M$ of any combinatorial optimization problem with a linear objective function is an affine image of a face of the cut polytope whose dimension is polynomial with respect to the dimension of $M$.

Keywords: combinatorial optimization, cut polytope, knapsack polytope, faces, polynomial reducibility of problems.

Full text: PDF file (197 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:8, 28–34

Bibliographic databases:

UDC: 519.854
Received: 28.06.2011

Citation: A. N. Maksimenko, “An analog of the Cook theorem for polytopes”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 8, 34–42; Russian Math. (Iz. VUZ), 56:8 (2012), 28–34

Citation in format AMSBIB
\Bibitem{Mak12}
\by A.~N.~Maksimenko
\paper An analog of the Cook theorem for polytopes
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 8
\pages 34--42
\mathnet{http://mi.mathnet.ru/ivm8729}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3077485}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 8
\pages 28--34
\crossref{https://doi.org/10.3103/S1066369X1208004X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866256976}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Seliverstov, “On monomials in quadratic forms”, J. Appl. Industr. Math., 7:3 (2013), 431–434  mathnet  crossref  mathscinet
    2. Fiorini S., Massar S., Patra M.K., Tiwary H.R., “Generalized Probabilistic Theories and Conic Extensions of Polytopes”, J. Phys. A-Math. Theor., 48:2 (2015), 025302  crossref  mathscinet  zmath  isi  elib
    3. A. N. Maksimenko, “A special role of Boolean quadratic polytopes among other combinatorial polytopes”, Model. i analiz inform. sistem, 23:1 (2016), 23–40  mathnet  crossref  mathscinet  elib
    4. A. N. Maksimenko, “Bulev kvadratichnyi mnogogrannik yavlyaetsya granyu mnogogrannika lineinykh poryadkov”, Sib. elektron. matem. izv., 14 (2017), 640–646  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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