Distributed fault-tolerant embeddings of rings in hypercubes
Journal of Parallel and Distributed Computing
Embedding a ring in a hypercube with both faulty links and faulty nodes
Information Processing Letters
Embedding of Rings and Meshes onto Faulty Hypercubes Using Free Dimensions
IEEE Transactions on Computers
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
Long paths in hypercubes with conditional node-faults
Information Sciences: an International Journal
Long paths in hypercubes with a quadratic number of faults
Information Sciences: an International Journal
Long paths and cycles in hypercubes with faulty vertices
Information Sciences: an International Journal
Longest fault-free paths in hypercubes with vertex faults
Information Sciences: an International Journal
Computational complexity of long paths and cycles in faulty hypercubes
Theoretical Computer Science
Embedded paths and cycles in faulty hypercubes
Journal of Combinatorial Optimization
Hamiltonian connectivity of restricted hypercube-like networks under the conditional fault model
Theoretical Computer Science
Hamiltonian cycles in hypercubes with faulty edges
Information Sciences: an International Journal
On the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty hypercube
Journal of Combinatorial Optimization
| Hi-index | 0.00 |
Let f(n) be the maximum integer such that for every set F of at most f(n) vertices of the hypercube Q n , there exists a cycle of length at least 2 n 驴2|F| in Q n 驴F. Castañeda and Gotchev conjectured that $f(n)=\binom{n}{2}-2$ . We prove this conjecture. We also prove that for every set F of at most (n 2+n驴4)/4 vertices of Q n , there exists a path of length at least 2 n 驴2|F|驴2 in Q n 驴F between any two vertices such that each of them has at most 3 neighbors in F. We introduce a new technique of potentials which could be of independent interest.