A bent Hamilton cycle in a grid graph is one in which each edge in a successive pair of edges lies in a different dimension. We show that the d-dimensional grid graph has a bent Hamilton cycle if some dimension is even and d ≥ 3, and does not have a bent Hamilton cycle if all dimensions are odd. In the latter case, we determine the conditions for when a bent Hamilton path exists. For the d-dime...

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 ...

In the paper we study lower bounds on the number of bent functions that can be obtained by iterative constructions, namely by the construction proposed by A. Canteaut and P. Charpin in 2003. The number of bent iterative functions is expressed in terms of sizes of finite sets and it is shown that evaluation of this number is closely connected to the problem of decomposing Boolean function into s...