Worst nearest-neighbor tour on a ten-vertex graph metric
TheoremDB P2706 · combinatorial optimization
Inferred from the community field; finer classification has not been reviewed.
Problem statement
For each connected simple graph on labeled vertices , use shortest-path distance as a complete metric. Starting at , repeatedly visit the nearest unvisited vertex, breaking ties by the smaller label, then return to . What is the largest ratio between this tour length and the optimal traveling-salesperson tour length?
Lean 4
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Progress & source assessment
Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution.
- [1]TheoremDB P2706 link
Recorded progress
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Discussion
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