$n$-dipath. We call such an oriented tree a *sink fountain tree* and call the $1$-page oriented book embedding described above a *sink fountain oriented book embedding*. We denote the spine order of a such an embedding $(x_1; \gamma_{x_1})^f$, where $x_1$ is the top vertex in the spine and $\gamma_{x_1}$ represents $(x_2,...,x_n, \alpha_n, \alpha_{n-1},..., \alpha_1)$. Similarly, we can construct a *source fountain tree*.

![Constructing a sink fountain tree[]{data-label="fig: fnt_tree"}](fountain_tree_combo.eps)

$1$-page Critical Oriented Graphs
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We now characterize the class, $\mathcal{M}^1$, of $1$-page critical oriented graphs. The only connected oriented graph on $n$ vertices which can be embedded into a $0$-page book, i.e., only the spine, is a directed path $\overrightarrow{P_n}$. Since $\overrightarrow{P_n}$ has exactly one source and exactly one sink, to find minimal obstructions, we consider oriented graphs having a source or sink of degree at least two. Thus we define $S^+$ to be the oriented $3$-path containing a source of degree two, and we define its converse $(S^+)^*$ to be $S^-$, which contains a sink of degree two. If an oriented graph is an oriented tree that is not an oriented path, it contains a vertex of degree greater than or equal to three and must also contain an oriented 