Tolerating Faults in Hypercubes Using Subcube Partitioning
IEEE Transactions on Computers - Special issue on fault-tolerant computing
Embedding a ring in a hypercube with both faulty links and faulty nodes
Information Processing Letters
A Survey of Combinatorial Gray Codes
SIAM Review
On ring embedding in hypercubes with faulty nodes and links
Information Processing Letters
Fault-tolerant cycle embedding in the hypercube
Parallel Computing
Longest paths and cycles in faulty hypercubes
PDCN'06 Proceedings of the 24th IASTED international conference on Parallel and distributed computing and networks
Cycles embedding in hypercubes with node failures
Information Processing Letters
Conditional edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Sciences: an International Journal
Edge-fault-tolerant bipanconnectivity of hypercubes
Information Sciences: an International Journal
Long paths in hypercubes with conditional node-faults
Information Sciences: an International Journal
Longest fault-free paths in hypercubes with vertex faults
Information Sciences: an International Journal
Embedded paths and cycles in faulty hypercubes
Journal of Combinatorial Optimization
Long paths in hypercubes with a quadratic number of faults
Information Sciences: an International Journal
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
Computational complexity of long paths and cycles in faulty hypercubes
Theoretical Computer Science
Conditional edge-fault-tolerant Hamiltonicity of dual-cubes
Information Sciences: an International Journal
Edge-fault-tolerant diameter and bipanconnectivity of hypercubes
Information Processing Letters
Independent spanning trees on even networks
Information Sciences: an International Journal
Efficient connectivity testing of hypercubic networks with faults
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Long cycles in hypercubes with optimal number of faulty vertices
Journal of Combinatorial Optimization
Edge-fault-tolerant panconnectivity and edge-pancyclicity of the complete graph
Information Sciences: an International Journal
Conditional edge-fault pancyclicity of augmented cubes
Theoretical Computer Science
Hamiltonian cycles in hypercubes with faulty edges
Information Sciences: an International Journal
Paired many-to-many disjoint path covers in faulty hypercubes
Theoretical Computer Science
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A fault-free path in the n-dimensional hypercube Q"n with f faulty vertices is said to be long if it has length at least 2^n-2f-2. Similarly, a fault-free cycle in Q"n is long if it has length at least 2^n-2f. If all faulty vertices are from the same bipartite class of Q"n, such length is the best possible. We show that for every set of at most 2n-4 faulty vertices in Q"n and every two fault-free vertices u and v satisfying a simple necessary condition on neighbors of u and v, there exists a long fault-free path between u and v. This number of faulty vertices is tight and improves the previously known results. Furthermore, we show for every set of at most n^2/10+n/2+1 faulty vertices in Q"n where n=15 that Q"n has a long fault-free cycle. This is a first quadratic bound, which is known to be asymptotically optimal.