Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 75, Issue 2 (2010), 678-710.
Some natural decision problems in automatic graphs
For automatic and recursive graphs, we investigate the following problems:
- (A) existence of a Hamiltonian path and existence of an infinite path in a tree
- (B) existence of an Euler path, bounding the number of ends, and bounding the number of infinite branches in a tree
- (C) existence of an infinite clique and an infinite version of set cover
- (A) are equally complex for automatic and for recursive graphs (Σ11-complete),
- (B) are moderately less complex for automatic than for recursive graphs (complete for different levels of the arithmetic hierarchy),
- (C) are much simpler for automatic than for recursive graphs (decidable and Σ11-complete, resp.).
J. Symbolic Logic, Volume 75, Issue 2 (2010), 678-710.
First available in Project Euclid: 18 March 2010
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Kuske, Dietrich; Lohrey, Markus. Some natural decision problems in automatic graphs. J. Symbolic Logic 75 (2010), no. 2, 678--710. doi:10.2178/jsl/1268917499. https://projecteuclid.org/euclid.jsl/1268917499