# Category:Arborescences

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This category contains results about Arborescences.

Definitions specific to this category can be found in Definitions/Arborescences.

Let $G = \left({V, A}\right)$ be a directed graph.

Let $r \in V$.

### Definition 1

$G$ is an **arborescence of root $r$** if and only if:

- For each $v \in V$ there is exactly one directed walk from $r$ to $v$.

### Definition 2

$G$ is an **arborescence of root $r$** if and only if:

- $(1): \quad$ $G$ is an orientation of a tree
- $(2): \quad$ For each $v \in V$, $v$ is reachable from $r$.

### Definition 3

$G$ is an **arborescence of root $r$** if and only if:

- $(1): \quad$ Each vertex $v \ne r$ is the final vertex of exactly one arc.
- $(2): \quad$ $r$ is not the final vertex of any arc.
- $(3): \quad$ For each $v \in V$ such that $v \ne r$ there is a directed walk from $r$ to $v$.

## Pages in category "Arborescences"

This category contains only the following page.