On the existence of Hamiltonian circuits in faulty hypercubes
SIAM Journal on Discrete Mathematics
Fault-tolerant hamiltonian laceability of hypercubes
Information Processing Letters
Fault-free Hamiltonian cycles in crossed cubes with conditional link faults
Information Sciences: an International Journal
Edge-bipancyclicity of conditional faulty hypercubes
Information Processing Letters
A fault-free Hamiltonian cycle passing through prescribed edges in a hypercube with faulty edges
Information Processing Letters
Edge-fault-tolerant bipanconnectivity of hypercubes
Information Sciences: an International Journal
Long paths in hypercubes with conditional node-faults
Information Sciences: an International Journal
Edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Processing Letters
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
Hamiltonian properties of honeycomb meshes
Information Sciences: an International Journal
The domination number of exchanged hypercubes
Information Processing Letters
| Hi-index | 0.07 |
In this paper we consider Hamiltonian cycles in hypercubes with faulty edges and present a simple proof that the hypercube Q"n is not Hamiltonian if it contains a subgraph T such that: (i) exactly half of the vertices in T have parity 0 (the other half have parity 1) and (ii) all edges joining the nodes of parity 0 (or 1) with nodes outside T, are faulty. We will call such a subgraph a trap disconnected halfway. Moreover, we show that for n=5, the cube Q"n with 2n-4 faulty edges is not Hamiltonian only if it contains a trap T disconnected halfway with T being a subcube of dimension 1 or 2.