How to prove that path in directed tree is directed path?

87 Views Asked by At

So I have a directed tree where I have a path that begins in the root of tree and leads to any vertex. I have to prove that this path is a directed path.

1

There are 1 best solutions below

0
On

In a directed tree the root has indegree $0$ and every vertex other than the root has indegree $1$.

Whence suppose we have a path $C$ that begins in the root and is not directed; consider the first vertex $v \in C$ in which the path is not directed: we obtain a contradiction.