On Copoint Graphs
Arts and Sciences
0000-0003-4666-9538, 0000-0002-6343-4362, 0000-0001-5914-2140
A convex geometry is a discrete abstraction of convexity defined by a meet-distributive lattice on a finite set. In particular, we study a graph formed from the copoints of a convex geometry. A graph that can be realized in this way from some convex geometry is called a copoint graph. We demonstrate existence and non-existence for several infinite families of graphs as copoint graphs. We show that the graph join of a copoint graph and a non-copoint graph is not a copoint graph. Further, we provide a construction to show that the complement of a copoint graph need not be a copoint graph. We conclude that not all trees are copoint graphs and argue that the Hasse diagram of a convex geometry has a `rhomboidal' structure if and only if its copoint graph is a tree.
Albert, Michael; Franchere, Evan; and Zomkyi, Tenzin, "On Copoint Graphs" (2019). Summer Interdisciplinary Research Symposium. 54.