A linear-time algorithm for finding Hamiltonian (s,t)-paths in even-sized rectangular grid graphs with a rectangular hole

The Hamiltonian path problem for general grid graphs is NP-complete. In this paper, we give the necessary conditions for the existence of a Hamiltonian path between two given vertices in a rectangular grid graph with a rectangular hole; where the size of graph is even. In addition, we show that the Hamiltonian path in these graphs can be computed in linear-time.