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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     author = {A. N. Maksimenko},
     title = {On the number of facets of a 2-neighborly polytope},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2010_17_1_a5/}
}
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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/