The Cyclic Cutwidth of $Q_n$

TL;DR

This paper investigates the cyclic cutwidth of n-dimensional hypercubes, focusing on the conjecture that Graycode numbering minimizes it, and presents partial results supporting this hypothesis.

Contribution

It advances understanding of the cyclic cutwidth in hypercubes and provides partial results towards proving the Graycode conjecture.

Findings

Partial results supporting the Graycode conjecture.

Insights into the structure of cyclic cutwidth in hypercubes.

Progress towards proving the minimality of Graycode numbering.

Abstract

In this article the cyclic cutwidth of the $n$-dimensional cube is explored. It has been conjectured by Dr. Chavez and Dr. Trapp that the cyclic cutwidth of $Q_n$ is minimized with the Graycode numbering. Several results have been found toward the proof of this conjecture.