Hamiltonicity of automatic graphs

@inproceedings{Kuske2008HamiltonicityOA,
  title={Hamiltonicity of automatic graphs},
  author={Dietrich Kuske and Markus Lohrey},
  booktitle={IFIP TCS},
  year={2008}
}
It is shown that the existence of a Hamiltonian path in a planar automatic graph of bounded degree is complete for ∑1 1, 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 ∑1 1… CONTINUE READING

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