Wikipedia
Multitree
In combinatorics and order-theoretic mathematics, a multitree may describe either of two equivalent structures: a directed acyclic graph in which the set of nodes reachable from any node form a tree, or a partially ordered set that does not have four items a, b, c, and d forming a diamond suborder with and but with b and c incomparable to each other (also called a diamond-free poset).