The number of Hamiltonian paths in a rectangular grid

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It is easy to find out which rectangular m vertex by n vertex grids have a Hamiltonian path from one corner to another using a checkerboard argument. However, it is quite difficult in general to count the total number of such paths. In this paper we give generating function answers for grids with fixed m for m = 1, 2, 3, 4, 5.




Collins, K. L., & Krompart, L. B. (1997). The number of Hamiltonian paths in a rectangular grid. Discrete Mathematics, 169(1–3), 29–38.

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