Odd generalization of trees?

When dealing with directed graphs, a tree is a graph in which every node except one (the root) has a single incoming edge? Are there any examples of treelike stru开发者_运维问答ctures in which every node has at most some constant number of incoming edges; say, at most two, or at most three? I haven't come across any graphs specifically described this way; is there a particular application in which they are used?

---

In graph theory, a tree is a connected acyclic graph. There is no requirement that every node have one incoming edge. In computer science, we often deal with rooted trees that agree with your definition.

Here is one description of a tree where some of the nodes have a constant number of incoming edges: an assignment of projects to employees, where each employee can be assigned at most three projects.

---

The most common generalization of a tree is a "DAG" (Directed Acyclic Graph) which is tangentially related but does not set a maximum on the size of in-neighborhoods (arcs which lead into a vertex) and specification of a single source (vertices with empty in-neighborhood).

From what I know, there's no neat term for what you're looking for. You'll need to find a true mathematician with a deep interest in graph theory to know with any certainty!

---

Lattices (partially ordered sets) have that property.