Hamiltonicity of automatic graphs

  • Dietrich Kuske
  • Markus Lohrey
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 273)

Abstract

It is shown that the existence of a Hamiltonian path in a planar automatic graph of bounded degree is complete for ∑11, the first level of the analytical hierarchy. This sharpens a corresponding result of Hirst and Harel for highly recursive graphs. Furthermore, we also show: (i) The Hamiltonian path problem for finite planar graphs that are succinctly encoded by an automatic presentation is NEXPTIME-complete, (ii) the existence of an infinite path in an automatic successor tree is ∑11-complete, and (iii) an infinite version of the set cover problem is decidable for automatic graphs (it is ∑11-complete for recursive graphs).

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Copyright information

© IFIP International Federation for Information Processing 2008

Authors and Affiliations

  • Dietrich Kuske
    • 1
  • Markus Lohrey
    • 1
  1. 1.Institut für InformatikUniversität LeipzigLeipzigGermany

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