The lower bound for the number of facets of a k-neighborly d-polytope with d+3 vertices

Abstract

We have found the minimal difference $\Delta (k)=\underset{P}{\min }(f_{d-1}(P)-f_0(P))$ between the number of facets and the number of vertices of a $k$-neighborly $d$-polytope $P$ for the case $f_0(P)=d+3$: $\Delta (2)=4$, $\Delta (3)=15$, and $\Delta (k)=2(k^2-1)$ for $k\ge 4$.

16 pages, 8 figures

References in corpus (2)

• Realizability and inscribability for simplicial polytopes via nonlinear optimization
• A special role of Boolean quadratic polytopes among other combinatorial polytopes

Cited by in corpus (2)

• 2-neighborly 0/1-polytopes of dimension 7
• On the minimum number of facets of a 2-neighborly polytope