The asymptotic diameter of cyclohedra

TL;DR

This paper establishes an upper bound on the diameter of d-dimensional cyclohedra and demonstrates that this bound is asymptotically sharp, providing insights into their geometric structure.

Contribution

It introduces a tight asymptotic bound on the diameter of cyclohedra, advancing understanding of their combinatorial properties.

Findings

Diameter of cyclohedra is at most ⌈5d/2⌉ - 2.

The upper bound's coefficient 5/2 is asymptotically sharp.

Diameter is at least 5d/2 - 4√d - 4.

Abstract

It is shown here that the diameter of the $d$-dimensional cyclohedron is not greater than $\lceil 5d/2\rceil-2$. It is also shown that the $5/2$ coefficient in this upper bound is asymptotically sharp. More precisely, the $d$-dimensional cyclohedron has diameter at least $5d/2-4\sqrt{d}-4$.