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- Published 1982 in SIAM J. Comput.

A grid graph is a node-induced finite subgraph of the infinite grid. It is rectangular if its set of nodes is the product of two intervals. Given a rectangular grid graph and two of its nodes, we give necessary and sufficient conditions for the graph to have a Hamilton path between these two nodes. In contrast, the Hamilton path (and circuit) problem for general grid graphs is shown to be NP-complete. This provides a new, relatively simple, proof of the result that the Euclidean traveling salesman problem is NP-complete.

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@article{Itai1982HamiltonPI,
title={Hamilton Paths in Grid Graphs},
author={Alon Itai and Christos H. Papadimitriou and Jayme Luiz Szwarcfiter},
journal={SIAM J. Comput.},
year={1982},
volume={11},
pages={676-686}
}