Embedding paths of variable lengths into hypercubes with conditional link-faults

Faults in a network may take various forms such as hardware failures while a node or a link stops functioning, software errors, or even missing of transmitted packets. In this paper, we study the link-fault-tolerant capability of an n-dimensional hypercube (n-cube for short) with respect to path embedding of variable lengths in the range from the shortest to the longest. Let F be a set consisting of faulty links in a wounded n-cube Qn, in which every node is still incident to at least two fault-free links. Then we show that Qn-F has a path of any odd (resp. even) length in the range from the distance to 2n-1 (resp. 2n-2) between two arbitrary nodes even if |F|=2n-5. In order to tackle this problem, we also investigate the fault diameter of an n-cube with hybrid node and link faults.