The Hamiltonian connectivity of rectangular supergrid graphs

Ruo-Wei Hung, Chin-Feng Li, Jong-Shin Chen, Qing-Song Su
2017 Discrete Optimization  
A Hamiltonian path of a graph is a simple path which visits each vertex of the graph exactly once. The Hamiltonian path problem is to determine whether a graph contains a Hamiltonian path. A graph is called Hamiltonian connected if there exists a Hamiltonian path between any two distinct vertices. In this paper, we will study the Hamiltonian connectivity of rectangular supergrid graphs. Supergrid graphs were first introduced by us and include grid graphs and triangular grid graphs as their
more » ... aphs. The Hamiltonian path problem for grid graphs and triangular grid graphs was known to be NP-complete. Recently, we have proved that the Hamiltonian path problem for supergrid graphs is also NP-complete. The Hamiltonian paths on supergrid graphs can be applied to compute the stitching traces of computer sewing machines. Rectangular supergrid graphs form a popular subclass of supergrid graphs, and they have strong structure. In this paper, we will show that rectangular supergrid graphs are Hamiltonian connected except two trivial forbidden conditions.
doi:10.1016/j.disopt.2017.06.001 fatcat:c7um4x3euzggpg4nzibjwvf3pq