## Hamiltonian paths in $$L$$-shaped grid graphs.(English)Zbl 1335.05100

Summary: Grid graphs are subgraphs of the infinite 2-dimensional integer grid. The Hamiltonian path problem for general grid graphs is a well-known NP-complete problem. In this paper, we present necessary and sufficient conditions for the existence of a Hamiltonian path between two given vertices in $$L$$-shaped grid graphs. We also show that a Hamiltonian path between two given vertices of a $$L$$-shaped grid graph can be computed in linear time.

### MSC:

 05C38 Paths and cycles 05C45 Eulerian and Hamiltonian graphs 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
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### References:

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