Trees as semilattices
Leonid O. Libkin, Vladimir A. Gurvich · Discrete Mathematics · 1995
We study semilattices whose diagrams are trees. First, we characterize them as semilattices whose convex subsemilattices form a convex geometry, or, equivalently, the closure induced by convex subsemilattices is antiexchange. Then we give lattice theoretic and two graph theoretic characterizations of atomistic semilattices with tree diagrams.