Abstract
The burnt pancake graph BPn is the Cayley graph of the hyperoctahedral group using prefix reversals as generators. Let {u,v} and {x,y} be any two pairs of distinct vertices of BPn for n≥4. We show that there are u−v and x−y paths whose vertices partition the vertex set of BPn even if BPn has up to n−4 faulty elements. On the other hand, for every n≥3 there is a set of n−2 faulty edges or faulty vertices for which such a fault-free disjoint path cover does not exist.
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