Topological Properties of Hypercubes
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Edge-pancyclic block-intersection graphs
Discrete Mathematics - Special volume: Designs and Graphs
Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes
Information Processing Letters
Graph Theory With Applications
Graph Theory With Applications
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A bipartite graph is bipancyclic if it contains a cycle of every even length from 4 to |V(G)| inclusive. A hamiltonian bipartite graph G is bipanpositionable if, for any two different vertices x and y, there exists a hamiltonian cycle C of G such that d"C(x,y)=k for any integer k with d"G(x,y)@?k@?|V(G)|/2 and (k-d"G(x,y)) being even. A bipartite graph G is k-cycle bipanpositionable if, for any two different vertices x and y, there exists a cycle of G with d"C(x,y)=l and |V(C)|=k for any integer l with d"G(x,y)@?l@?k2 and (l-d"G(x,y)) being even. A bipartite graph G is bipanpositionable bipancyclic if G is k-cycle bipanpositionable for every even integer k, 4@?k@?|V(G)|. We prove that the hypercube Q"n is bipanpositionable bipancyclic for n=2.