Paired 3-disjoint path covers of balanced hypercubes

TL;DR

This paper establishes the existence of paired 3-disjoint path covers in balanced hypercubes, extending known results for 1- and 2-disjoint path covers and contributing to the understanding of hypercube connectivity.

Contribution

The paper proves the paired 3-disjoint path cover for balanced hypercubes, advancing the knowledge of their path cover properties beyond previous 1- and 2-disjoint results.

Findings

Paired 3-disjoint path cover exists for $BH_{n}$ with $n extgreater=3$.

Improves previous results on paired $k$-disjoint path covers for $k=1,2$.

Enhances understanding of balanced hypercube connectivity and fault tolerance.

Abstract

The balanced hypercube $BH_{n}$, proposed by Wu and Huang, is a variation of the hypercube. The paired 1-disjoint path cover of $BH_{n}$ is the Hamiltonian laceability, which was obtained by Xu et al. in [Appl. Math. Comput. 189 (2007) 1393--1401]. The paired 2-disjoint path cover of $BH_{n}$ was obtained by Cheng et al. in [Appl. Math. and Comput. 242 (2014) 127-142]. In this paper, we obtain the paired 3-disjoint path cover of $BH_{n}$ with $n\geq 3$. This result improves the above known results about the paired $k$-disjoint path covers of $BH_{n}$ for $k=1,2$.