Hamiltonian cycles passing through linear forests in k-ary n-cubes

doi:10.1016/j.dam.2011.05.008

Discrete Applied Mathematics

Volume 159, Issue 14, 28 August 2011, Pages 1425-1435

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Abstract

The $k$ -ary $n$ -cube is one of the most popular interconnection networks for parallel and distributed systems. A linear forest in a graph is a subgraph, each component of which is a path. In this paper, we investigate the existence of Hamiltonian cycles passing through linear forests in the $k$ -ary $n$ -cube. For any $n \geq 2$ and $k \geq 3$ , we show that the $k$ -ary $n$ -cube admits a Hamiltonian cycle passing through a linear forest with at most $2 n - 1$ edges.

Highlights

► The $k$ -ary $n$ -cube admits a Hamiltonian cycle passing through a prescribed linear forest. ► The number of edges in the prescribed linear forest does not exceed $2 n - 1$ . ► This generalized Dvor˘ák’s results.

Keywords

Interconnection networks

k

-ary

n

-cubes

Hamiltonian cycles

Linear forests

Cited by (0)

^☆: This work is supported by the National Natural Science Foundation of China (61070229, 11026163) and the Program of Shanxi Province for Postgraduates’ Innovation (20103012).

Discrete Applied Mathematics

Hamiltonian cycles passing through linear forests in k-ary n-cubes☆

Abstract

Highlights

Keywords

Hamiltonian cycles passing through linear forests in $k$ -ary $n$ -cubes☆