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Diskr. Mat., 2008, Volume 20, Issue 1, Pages 64–69 (Mi dm989)  

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

On random 2-adjacent 0/1-polyhedra

V. A. Bondarenko, A. G. Brodskiy


Abstract: We estimate the probability $P_{k,m}$ that, as $k$ vertices of the unit cube $I_m=\{0,1\}^m$ are randomly chosen, their convex hull is a polyhedron whose graph is complete. In particular, we establish that, as $n\to\infty$, the probability $P_{k(m),m}$ tends to one if $k(m)=O(2^{m/6})$ and $P_{k(m),m}$ tends to zero if $k(m)\geq(3/2)^m$.
The results given in this paper, first, to a great extent explain why the intractable discrete problems are so widely spread, and second, support the well-known Gale's hypothesis published in 1956.

DOI: https://doi.org/10.4213/dm989

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English version:
Discrete Mathematics and Applications, 2008, 18:2, 181–186

Bibliographic databases:

UDC: 519.1
Received: 15.01.2006
Revised: 21.07.2006

Citation: V. A. Bondarenko, A. G. Brodskiy, “On random 2-adjacent 0/1-polyhedra”, Diskr. Mat., 20:1 (2008), 64–69; Discrete Math. Appl., 18:2 (2008), 181–186

Citation in format AMSBIB
\Bibitem{BonBro08}
\by V.~A.~Bondarenko, A.~G.~Brodskiy
\paper On random 2-adjacent 0/1-polyhedra
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 1
\pages 64--69
\mathnet{http://mi.mathnet.ru/dm989}
\crossref{https://doi.org/10.4213/dm989}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2420497}
\zmath{https://zbmath.org/?q=an:1178.90250}
\elib{http://elibrary.ru/item.asp?id=20730229}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 2
\pages 181--186
\crossref{https://doi.org/10.1515/DMA.2008.014}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-44449094679}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Brodskii, “O 2-smezhnostnykh mnogogrannikakh i konstruktsii Geila”, Model. i analiz inform. sistem, 16:2 (2009), 5–20  mathnet
    2. A. N. Maksimenko, “O chisle faset 2-smezhnostnogo mnogogrannika”, Model. i analiz inform. sistem, 17:1 (2010), 76–82  mathnet
    3. A. G. Brodskii, “Dvoistvennost Geila i smezhnostnost sluchainykh mnogogrannikov. II”, Model. i analiz inform. sistem, 19:4 (2012), 87–109  mathnet
    4. A. N. Maksimenko, “$k$-neighborly faces of the Boolean quadric polytopes”, J. Math. Sci., 203:6 (2014), 816–822  mathnet  crossref  mathscinet
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