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Durham University

Computer Science


Publication details for Professor Iain Stewart

Stewart, I.A. (2011), Hamiltonian cycles through prescribed edges in k-ary n-cubes, in Wang, W., Zhu, X. & Du, D.-Z. eds, Lecture Notes in Computer Science Vol. 6831 6831: 5th Annual International Conference on Combinatorial Optimization and Applications, COCOA'11. Zhangjiajie, China, Springer, Berlin, 82-97.

Author(s) from Durham


We prove that if P is a set of at most 2n − 1 edges in a k-ary n-cube, where k ≥ 4 and n ≥ 2, then there is a Hamiltonian cycle on which every edge of P lies if, and only if, the subgraph of the k-ary n-cube induced by the edges of P is a vertex-disjoint collection of paths. This answers a question posed by Wang, Li and Wang who proved the analogous result for 3-ary n-cubes.