Hamiltonian laceability of bubble-sort graphs with edge faults

  • Authors:

  • Toru Araki;Yosuke Kikuchi

  • Affiliations:

  • Department of Computer and Information Sciences, Iwate University, 4-3-5 Ueda, Morioka, Iwate 020-8551, Japan;Department of Electronics and Computer Engineering, Tsuyama National College of Technology, Tsuyama, Okayama 708-8509, Japan

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

It is known that the n-dimensional bubble-sort graph B"n is bipartite, (n-1)-regular, and has n! vertices. We first show that, for any vertex v, B"n-v has a hamiltonian path between any two vertices in the same partite set without v. Let F be a subset of edges of B"n. We next show that B"n-F has a hamiltonian path between any two vertices of different partite sets if |F| is at most n-3. Then we also prove that B"n-F has a path of length n!-2 between any pair of vertices in the same partite set.