Abstract
The Bubble-sort graph BSn,n⩾2, is a Cayley graph over the symmetric group Symn generated by transpositions from the set {(12),(23),…,(n−1n)}. It is a bipartite graph containing all even cycles of length ℓ, where 4⩽ℓ⩽n!. We give an explicit combinatorial characterization of all its 4- and 6-cycles. Based on this characterization, we define generalized prisms in BSn,n⩾5, and present a new approach to construct a Hamiltonian cycle based on these generalized prisms.
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