Hamiltonian cycles of balanced hypercube with more faulty edges

TL;DR

This paper proves the existence of fault-free Hamiltonian cycles in balanced hypercubes with more faulty edges than previously known, under certain conditions, enhancing the understanding of their fault tolerance.

Contribution

It improves existing bounds on the number of faulty edges in balanced hypercubes that still allow Hamiltonian cycles, considering degree and cycle constraints.

Findings

Hamiltonian cycle exists with up to 5n-7 faulty edges.

Fault tolerance is improved under degree and cycle restrictions.

Results extend the known fault tolerance bounds for balanced hypercubes.

Abstract

The balanced hypercube $BH_{n}$, a variant of the hypercube, is a novel interconnection network for massive parallel systems. It is known that the balanced hypercube remains Hamiltonian after deleting at most $4n-5$ faulty edges if each vertex is incident with at least two edges in the resulting graph for all $n\geq2$. In this paper, we show that there exists a fault-free Hamiltonian cycle in $BH_{n}$ for $n\ge 2$ with $\left | F \right |\le 5n-7$ if the degree of every vertex in $BH_{n}-F$ is at least two and there exists no $f_{4}$-cycles in $BH_{n}-F$, which improves some known results.