On the existence of Hamiltonian circuits in faulty hypercubes
SIAM Journal on Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Complexity of Problems Concerning Graphs with Regularities (Extended Abstract)
Proceedings of the Mathematical Foundations of Computer Science 1984
Fault-tolerant cycle embedding in the hypercube
Parallel Computing
Hamiltonian Cycles with Prescribed Edges in Hypercubes
SIAM Journal on Discrete Mathematics
Partitions of Faulty Hypercubes into Paths with Prescribed Endvertices
SIAM Journal on Discrete Mathematics
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
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
On the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty hypercube
Journal of Combinatorial Optimization
| Hi-index | 5.23 |
The problem of existence of an optimal-length (long) fault-free cycle in the n-dimensional hypercube with f faulty vertices is NP-hard. This holds even in case that f is bounded by a polynomial of degree three (six) with respect to n. On the other hand, there is a linear (quadratic) bound on f which guarantees that the problem is decidable in polynomial time. Similar results are obtained for paths as well as for paths between prescribed endvertices.