On the number of facets of a 2-neighborly polytope
A d-polytope P is 2-neighborly if each 2 vertices of P determine an edge. It is conjectured that the number f<sub></sub><sub>0</sub>(P) of vertices for such polytope does not exceed the number f<sub></sub><sub>d-1</sub>(P) of facets. The conjecture is separately proved for d < 7 and for f<sub></sub><sub>0</sub>(P) < d+6.