Hamiltonicity of automatic graphs
نویسندگان
چکیده
It is shown that the existence of a Hamiltonian path in a planar automatic graph of bounded degree is complete for Σ1 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 Σ1 1 -complete, and (iii) an infinite version of the set cover problem is decidable for automatic graphs (it is Σ 1 1 -complete for recursive graphs).
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تاریخ انتشار 2008