Hamiltonian s–t paths in solid grid graphs are decidable in polynomial time
A computable algorithm, decideHamPath, that decides whether a solid grid graph (a finite set of lattice points with no holes, with an edge between points at distance 1) has a Hamiltonian path between two given distinct points, with a Lean 4 proof that it is correct. The problem was posed by Itai, Papadimitriou and Szwarcfiter (1982). The algorithm extends Sheffield's height-function algorithm for Hamiltonian cycles: each endpoint gets a phantom edge to a missing neighbour, and an endpoint with all eight neighbours present becomes a hole whose defect (a vortex) is handled by a slit height and…
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