Geodesic
On the number of facets of a 2-neighborly polytope
Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 1, pp. 76-82.

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A $d$-polytope $P$ is $2$-neighborly if each $2$ vertices of $P$ determine an edge. It is conjectured that the number $f_0(P)$ of vertices for such polytope does not exceed the number $f_{d-1}(P)$ of facets. The conjecture is separately proved for $d7$ and for $f_0(P)$.
Keywords: 2-neighborly polytopes, number of facets. 
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A. N. Maksimenko. On the number of facets of a 2-neighborly polytope. Modelirovanie i analiz informacionnyh sistem, Tome 17 (2010) no. 1, pp. 76-82. http://geodesic.mathdoc.fr/item/MAIS_2010_17_1_a5/

[1] V. A. Bondarenko, A. G. Brodskii, “O sluchainykh 2-smezhnostnykh 0/1-mnogogrannikakh”, Diskretnaya matematika, 20:1 (2008), 64–69 | MR | Zbl

[2] V. A. Bondarenko, A. N. Maksimenko, Geometricheskie konstruktsii i slozhnost v kombinatornoi optimizatsii, LKI, M., 2008, 184 pp.

[3] M. M. Deza, M. Loran, Geometriya razrezov i metrik, MTsNMO, M., 2001, 736 pp.

[4] V. A. Emelichev, M. M. Kovalev, M. K. Kravtsov, Mnogogranniki, grafy, optimizatsiya, Nauka, M., 1981, 344 pp. | MR

[5] O. Aichholzer, “Extremal properties of 0/1-polytopes of dimension 5”, Polytopes - Combinatorics and Computation, eds. G. Ziegler and G. Kalai, Birkhauser, 2000, 111–130 | MR | Zbl

[6] D. Avis, lrslib Ver 4.2 is a self-contained ANSI C implementation as a callable library of the reverse search algorithm for vertex enumeration/convex hull problems:, http://cgm.cs.mcgill.ca/~avis/C/lrs.html

[7] D. Barnette, “The minimum number of vertices of a simple polytope ”, Israel J. Math., 10 (1971), 121–125 | DOI | MR | Zbl

[8] D. Barnette, “A proof for the lower bound conjecture for convex polytopes”, Pacific J. Math., 46 (1973), 349–354 | MR | Zbl

[9] T. Bisztriczky, “On sewing neighbourly polytopes”, Note di Matematica, 20:1 (2000/2001), 73–80 | MR | Zbl

[10] G. Blind, R. Blind, “Convex polytopes without triangular faces”, Isr. J. Math., 71 (1990), 129–134 | DOI | MR | Zbl

[11] D. Gale, “Neighboring vertices on a convex polyhedron”, Linear inequalities and related systems, eds. H. W. Kuhn, A. W. Tucker, Princeton University Press, Princeton, New Jersey, 1956 | MR

[12] M. Henk, J. Richter-Gebert, G. Ziegler “Basic properties of convex polytopes”, Handbook of Discrete and Computational Geometry, Chapter 16, second edition, eds. J. E. Goodman and J. O'Rourke, Chapman Hall/CRC Press, Boca Raton, 2004, 355–382

[13] M. Kovalev, J.-F. Maurras, Y. Vaxes, “On the convex hull of 3-cycles of the complete graph ”, Pesquisa Operacional, 23:1 (2003), 99–109 | DOI

[14] S. Onn, “Geometry, Complexity, and Combinatorics of Permutation Polytopes”, J. Comb. Theory Series A, 64:1 (1993), 31–49 | DOI | MR | Zbl

[15] I. Shemer, “Neighborly polytopes”, Isr. J. Math., 43 (1982), 291–314 | DOI | MR | Zbl