Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6875484 | Theoretical Computer Science | 2018 | 8 Pages |
Abstract
Kreweras conjectured that every perfect matching in a hypercube Qn for nâ¥2 extends to a hamiltonian cycle of Qn. Fink confirmed the conjecture to be true. The k-ary n-cube Qnk is a generalization of the hypercube. However, the analogous result does not necessarily hold for Qnk. We can find a perfect matching in Q26 which is not contained in any hamiltonian cycle of Q26. In this paper, we investigate the existence of a hamiltonian cycle passing through a perfect matching in Qnk. For an integer nâ¥2 and an even integer kâ¥6, we prove that every perfect matching in Qnk consisting of edges in the same dimension can be extended to a hamiltonian cycle of Qnk.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Fan Wang, Wuyang Sun,