Bent Hamilton Cy les in d-Dimensional Grid Graphs
چکیده
F. Ruskey Joe Sawada y May 15, 2002 Abstra t A bent Hamilton y le in a grid graph is one in whi h ea h edge in a su essive pair of edges lies in a di erent dimension. We show that the d-dimensional grid graph has a bent Hamilton y le if some dimension is even and d 3, and does not have a bent Hamilton y le if all dimensions are odd. In the latter ase, we determine the onditions for when a bent Hamilton path exists. For the d-dimensional toroidal grid graph (i.e., the graph produ t of d y les), we show that there exists a bent Hamilton y le when all dimensions are odd and d 3. We also show that if d = 2, then there exists a bent Hamilton y le if and only if both dimensions are even.