Fault-tolerant embedding of complete binary trees in hypercubes

The focus is on the following graph-theoretic question associated with the simulation of complete binary trees by faulty hypercubes: if a certain number of nodes or links are removed from an n-cube, will an (n-1)-tree still exists as a subgraph? While the general problem of determining whether a k-tree, k< n, still exists when an arbitrary number of nodes/links are removed from the n-cube is found to be NP-complete, an upper bound is found on how many nodes/links can be removed and an (n-1)-tree still be guaranteed to exist. In fact, as a corollary of this, it is found that if no more than n-3 nodes/links are removed from an (n-1)-subcube of the n-cube, an (n-1)-tree is also guaranteed to exist