Abstract: We call a point set S in the nxn integer grid (geometric) dominating set if each point in the nxn grid is in the set S itself or lies on a common line with at least two points from the set. Our goal is to determine the minimum size of dominating sets in the nxn grid, which we call (geometric) domination number. First, I will present (asymptotic) lower and upper bounds on the domination number in the nxn grid. Then, I will generalize the problem to the discrete torus and prove asymptotic lower and upper bounds with probabilistic methods. In this context, we will also discuss a conjecture by Richard Guy and Patrick Kelly from the 1960s concerning the No-Three-In-Line problem, which asks for the maximum number of points in the nxn grid, so that no three points lie on a common line.
Zoom-Meeting beitreten:
https://zoom.us/j/95912775337?pwd=dWRrYjJPanJCQkRpUWI5WG9OeWpEdz09
Meeting-ID: 959 1277 5337
Kenncode: 4cX65L