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# 🔗 Hamiltonian Path

Band 8 — The Sol transformer. Visit every vertex exactly once.

Vertices: 7
Ready

### Algorithm: Backtracking Search

Try every vertex as start, recursively extend the path, prune when no unvisited neighbour exists. O(n!) worst case, but dense graphs prune quickly. This solver limits to 12 vertices for reasonable response times.

### Why This Matters

The Hamiltonian Path transformer (Sol, Band 8) finds the order that visits every node once — routing, genome assembly, and sequencing all reduce to this.