Fault-tolerant hamiltonian laceability of hypercubes

  • Authors:

  • Chang-Hsiung Tsai;Jimmy J. M. Tan;Tyne Liang;Lih-Hsing Hsu

  • Affiliations:

  • Department of Computer and Information Science, National Chiao Tung University, Hsinchu, 30050 Taiwan, ROC;Department of Computer and Information Science, National Chiao Tung University, Hsinchu, 30050 Taiwan, ROC;Department of Computer and Information Science, National Chiao Tung University, Hsinchu, 30050 Taiwan, ROC;Department of Computer and Information Science, National Chiao Tung University, Hsinchu, 30050 Taiwan, ROC

  • Venue:
  • Information Processing Letters
  • Year:
  • 2002

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Abstract

It is known that every hypercube Qn is a bipartite graph. Assume that n ≥ 2 and F is a subset of edges with |F| ≤ n - 2. We prove that there exists a hamiltonian path in Qn - F between any two vertices of different partite sets. Moreover, there exists a path of length 2n - 2 between any two vertices of the same partite set. Assume that n ≥ 3 and F is a subset of edges with |F| ≤ n - 3. We prove that there exists a hamiltonian path in Qn - {υ} - F between any two vertices in the partite set without υ. Furthermore, all bounds are tight.