Israel Journal of Mathematics

, Volume 76, Issue 3, pp 317–336 | Cite as

Hamiltonian paths in infinite graphs

  • David Harel


A tight connection is exhibited between infinite paths in recursive trees and Hamiltonian paths in recursive graphs. A corollary is that determining Hamiltonicity in recursive graphs is highly undecidable, viz, Σ 1 1 -complete. This is shown to hold even for highly recursive graphs with degree bounded by 3. Hamiltonicity is thus an example of an interesting graph problem that is outside the arithmetic hierarchy in the infinite case.


Internal Node Incident Edge Hamiltonian Path Recursive Tree Infinite Graph 
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Copyright information

© Hebrew University 1991

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computer ScienceThe Weizmann Institute of ScienceRehovotIsrael

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