On the existence of Hamiltonian circuits in faulty hypercubes
SIAM Journal on Discrete Mathematics
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Fault-Free Hamiltonian Cycles in Faulty Arrangement Graphs
IEEE Transactions on Parallel and Distributed Systems
Spanning graphs of hypercubes: starlike and double starlike trees
Discrete Mathematics - Algebraic and topological methods in graph theory
Linear array and ring embeddings in conditional faulty hypercubes
Theoretical Computer Science
Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty Edges
IEEE Transactions on Computers
Conditional edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Sciences: an International Journal
Edge-bipancyclicity of a hypercube with faulty vertices and edges
Discrete Applied Mathematics
Conditional Edge-Fault Hamiltonicity of Matching Composition Networks
IEEE Transactions on Parallel and Distributed Systems
Optimal fault-tolerant Hamiltonicity of star graphs with conditional edge faults
The Journal of Supercomputing
Conditional edge-fault Hamiltonicity of augmented cubes
Information Sciences: an International Journal
Pancyclicity and bipancyclicity of conditional faulty folded hypercubes
Information Sciences: an International Journal
Pancyclicity of Restricted Hypercube-Like Networks under the Conditional Fault Model
SIAM Journal on Discrete Mathematics
Spanning subgraphs of a hypercube II: Double starlike trees
Mathematical and Computer Modelling: An International Journal
Spanning subgraphs of a hypercube IV: Rooted trees
Mathematical and Computer Modelling: An International Journal
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An n-dimensional hypercube Q"n is a Hamiltonian graph; in other words Q"n (n=2) contains a spanning subgraph which is 2-regular and 2-connected. In this paper, we explore yet another strong property of hypercubes. We prove that for any integer k with 3@?k@?n, Q"n (n=3) contains a spanning subgraph which is k-regular, k-connected and bipancyclic. We also obtain the result that every mesh P"mxP"n (m,n=2) is bipancyclic, which is used to prove the property above.