into the spine, i.e., each vertex *must* be loose in the embedding. They prove that every oriented tree has a $1$-page oriented book embedding such that an arbitrarily chosen vertex, called the *root* is uncovered. We translate their result below.

\[oriented tree\] $($Heath, Pemmaraju, and Trenk, $1999$  [@SQLptI] $)$ For every oriented tree $\overrightarrow{T}$ with arbitrarily chosen root $v$, there exists a spine order of $V(\overrightarrow{T})$ that yields a $1$-page oriented book embedding of $\overrightarrow{T}$ in which the root $v$ is uncovered, every vertex is loose, and the page is upwards.

The above result only proves existence. We give an algorithm, called the riented ree pine rder Algorithm, or OTSO Algorithm, that gives a spine order which yields a $1$-page oriented book embedding as described in Theorem \[oriented tree\]. For convenience, we will always assume the direction of the page to be upwards, unless otherwise noted. For an oriented tree $\overrightarrow{T}$, we can choose the root to be a sink in $\overrightarrow{T}$. The following lemma proves that, in a $1$-page oriented book embedding of $\overrightarrow{T}$, we can place the root so that it is the top vertex in the spine.

An oriented tree $\overrightarrow{T}$, an arbitrarily fixed vertex $x \in 