The general position number of integer lattices

• The general position number of all integer grids is determined. Only very partial results were known earlier, each them required quite some effort to obtain it. main result also implies a lower bound on the multidimensional torus graphs. gp( G ) connected graph cardinality largest set S vertices such that no three pairwise distinct from lie common geodesic. n -dimensional grid P ∞ Cartesian product copies two-way infinite path . It proved if ∈ N , then gp ( = 2 − 1 was earlier only for {1, 2} and partially 3