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
Fault-tolerant hamiltonian laceability of hypercubes
Information Processing Letters
Conditional Connectivity Measures for Large Multiprocessor Systems
IEEE Transactions on Computers
Embedding of Rings and Meshes onto Faulty Hypercubes Using Free Dimensions
IEEE Transactions on Computers
Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes
Information Processing Letters
Fault-tolerant cycle embedding in the hypercube
Parallel Computing
Linear array and ring embeddings in conditional faulty hypercubes
Theoretical Computer Science
Optimal Path Embedding in Crossed Cubes
IEEE Transactions on Parallel and Distributed Systems
Cycles embedding in hypercubes with node failures
Information Processing Letters
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
Long paths in hypercubes with conditional node-faults
Information Sciences: an International Journal
Edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Processing Letters
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The hypercube is one of the best known interconnection networks. Embedding cycles of all possible lengths in faulty hypercubes has received much attention. Let F"v (respectively, F"e) denote the set of faulty vertices (respectively, faulty edges) and f"v (respectively, f"e) denote the number of faulty vertices (respectively, faulty edge) in an n-dimensional hypercube Q"n. Let f(e) denote the number of faulty nodes and/or faulty edges incident with the end-vertices of an edge e@?E(Q"n). In this paper, we assume that each node is incident with at least three fault-free neighbors and at least three fault-free edges. Under this assumption, we show that every fault-free edge lies on a fault-free cycle of every even length from 4 to 2^n-2|F"v| if |F"v|+|F"e|==5. Under our condition, our result not only improves the previously best known result of Hsieh et al. [S.-Y. Hsieh, T.-H. Shen, Edge-bipancyclicity of a hypercube with faulty vertices and edges, Discrete Applied Mathematics 156 (10) (2008) 1802-1808] where f"v+f"e=