On Hamiltonian Properties of Grid Graph

Abstract

This paper addresses the problem constructing a Hamilton cycle in the grid graph. For the general grid graphs, this task is known to be NP-complete [A. Itai et.al [2]]. We propose a sufficient condition only for having a Hamilton cycle in a grid graph and a corresponding algorithm has been constructed. We generalize the result of Yingtai Xie [The Hamiltonian properties of rectangular meshes with at most two faulty nodes, Yingtai Xie 2020 J. Phys.: Conf. Ser.1646 012044].