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.
2026-05-06 01:38:00.1778031480
How to prove that path in directed tree is directed path?
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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.