Fault-Tolerant Embeddings of Hamiltonian Circuits in k-ary n-Cubes
SIAM Journal on Discrete Mathematics
Lee Distance and Topological Properties of k-ary n-cubes
IEEE Transactions on Computers
Hamiltonian circuit and linear array embeddings in faulty k-ary n-cubes
Journal of Parallel and Distributed Computing
Cycles passing through prescribed edges in a hypercube with some faulty edges
Information Processing Letters
Hamiltonian cycles and paths with a prescribed set of edges in hypercubes and dense sets
Journal of Graph Theory
A fault-free Hamiltonian cycle passing through prescribed edges in a hypercube with faulty edges
Information Processing Letters
Bipanconnectivity and Bipancyclicity in k-ary n-cubes
IEEE Transactions on Parallel and Distributed Systems
Graph Theory
Edge-pancyclicity of Möbius cubes
Information Processing Letters
Complete path embeddings in crossed cubes
Information Sciences: an International Journal
Hamiltonian cycles through prescribed edges in k-ary n-cubes
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Hamiltonian properties of honeycomb meshes
Information Sciences: an International Journal
Fault-free Hamiltonian cycles passing through a linear forest in ternary n-cubes with faulty edges
Theoretical Computer Science
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The k-ary n-cube has been one of the most popular interconnection networks for massively parallel systems. Given a set P of at most 2n-2 (n=2) prescribed edges and two vertices u and v, we show that the 3-ary n-cube contains a Hamiltonian path between u and v passing through all edges of P if and only if the subgraph induced by P consists of pairwise vertex-disjoint paths, none of them having u or v as internal vertices or both of them as end-vertices. As an immediate result, the 3-ary n-cube contains a Hamiltonian cycle passing through a set P of at most 2n-1 prescribed edges if and only if the subgraph induced by P consists of pairwise vertex-disjoint paths.