Multitree

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 $a \leq b \leq d$ and $a \leq c \leq d$ but with $b$ and $c$ incomparable to each other (also called a diamond-free poset).

In computational complexity theory, multitrees have also been called strongly unambiguous graphs or mangroves; they can be used to model nondeterministic algorithms in which there is at most one computational path connecting any two states.

Multitrees may be used to represent multiple overlapping taxonomies over the same ground set. If a family tree may contain multiple marriages from one family to another, but does not contain marriages between any two blood relatives, then it forms a multitree.

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