Abstract
It is known that the n-dimensional bubble-sort graph B n is bipartite, ( n − 1)-regular, and has n! vertices. We first show that, for any vertex v, B n − v has a hamiltonian path between any two vertices in the same partite set without v. Let F be a subset of edges of B n . We next show that B n − F has a hamiltonian path between any two vertices of different partite sets if ∣ F∣ is at most n − 3. Then we also prove that B n − F has a path of length n! − 2 between any pair of vertices in the same partite set.
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