Wang, Fan; Zhang, Heping Matchings extend to Hamiltonian cycles in \(k\)-ary \(n\)-cubes. (English) Zbl 1360.68652 Inf. Sci. 305, 1-13 (2015). Summary: The \(k\)-ary \(n\)-cube is one of the most popular interconnection networks for parallel and distributed systems. Given an edge set in the \(k\)-ary \(n\)-cube, which conditions guarantee the existence of a Hamiltonian cycle in the \(k\)-ary \(n ~\)-cube containing the edge set? In this paper, we prove for \(n\geqslant 2\) and \(k\geqslant 3\) that every matching having at most \(3n-8\) edges is contained in a Hamiltonian cycle in the \(k\)-ary \(n\)-cube. Also, we present an example to show that the analogous conclusion does not hold for perfect matchings. Cited in 4 Documents MSC: 68R10 Graph theory (including graph drawing) in computer science 05C38 Paths and cycles 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) Keywords:interconnection network; \(k\)-ary \(n\)-cube; Hamiltonian cycle; perfect matching; matching PDFBibTeX XMLCite \textit{F. Wang} and \textit{H. Zhang}, Inf. Sci. 305, 1--13 (2015; Zbl 1360.68652) Full Text: DOI