Minimal change list for Lucas strings and some graph theoretic consequences

  • Authors:
  • Jean-Luc Baril;Vincent Vajnovszki

  • Affiliations:
  • Université de Bourgogne, Dijon-Cedex, France;Université de Bourgogne, Dijon-Cedex, France

  • Venue:
  • Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
  • Year:
  • 2005

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Abstract

We give a minimal change list for the set of order p length-n Lucas strings, i.e., the set of length-n binary strings with no p consecutive 1's nor a 1l prefix and a 1m suffix with l+m ≥ p. The construction of this list proves also that the order p n-dimensional Lucas cube has a Hamiltonian path if and only if n is not a multiple of p + 1, and its second power always has a Hamiltonian path.