All 2-neighborly d-polytopes with at most d + 9 facets

2019/12/09 by A. N. Maksimenko, Maksimenko, Aleksandr N., D. V. Gribanov +2
Engineering · Mathematics · #52Bxx #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Point processes and geometric inequalities #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1912.03900

openalex publication_date 2019/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a complete enumeration of all 2-neighborly d-polytopes with d+9 and less facets. All of them are realized as 0/1-polytopes, except a 6-polytope P_6,10,15 with 10 vertices and 15 facets, and pyramids over P_6,10,15. In particular, we update the lower bounds for the number of facets of a 2-neighborly d-polytope P and showed that the number of facets of P is not less than the number of its vertices f₀(P) for f₀(P) ≤ d + 10.

Citations

• 2-neighborly 0/1-polytopes of dimension 7

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