On arc-disjoint Hamiltonian cycles in De Bruijn graphs

TL;DR

This paper explores the problem of finding multiple arc-disjoint Hamiltonian cycles in De Bruijn graphs, providing two equivalent formulations of a related conjecture to advance understanding in graph theory.

Contribution

It introduces two equivalent formulations of a conjecture regarding arc-disjoint Hamiltonian cycles in De Bruijn graphs, offering new perspectives for future research.

Findings

Two equivalent formulations of the conjecture are presented.

The formulations provide new avenues for proving or disproving the conjecture.

The work advances theoretical understanding of Hamiltonian cycles in De Bruijn graphs.

Abstract

We give two equivalent formulations of a conjecture [2,4] on the number of arc-disjoint Hamiltonian cycles in De Bruijn graphs.