Multitree

Summary

In combinatorics and order theory, a multitree may describe either of two equivalent structures: a directed acyclic graph (DAG) in which there is at most one directed path between any two vertices, or equivalently in which the subgraph reachable from any vertex induces an undirected tree, or a partially ordered set (poset) that does not have four items $a$, $b$, $c$, and $d$ forming a diamond suborder with $a \le b \le d$ and $a \le c \le d$ but with $b$ and $c$ incomparable to each other (also called a diamond-free poset).