of $u$ as $N^+(u)$. We also say that the [*in-degree*]{} of $u$ is $|N^-(u)|$ and the [*out-degree*]{} of $u$ is $|N^+(u)|$. The [*neighborhood*]{} of $u$ is defined to be $N(u) := N^+(u) \cup N^-(u)$, and the [*degree*]{} of $u$ is $|N^-(u) \cup N^+(u)|$. If $N(u) = N^-(u)$, then $u$ is said to be a [*sink*]{}; if $N(u) = N^+(u)$, then $u$ is said to be a [*source*]{}.

For a graph $D$ with edge $e$, the [*deletion of $e$*]{} is an operation that yields a graph with edge set $E(D) \setminus e$ and vertex set $V(D)$. We denote the graph $D$ with edge $e$ deleted as $D \setminus e$. The deletion of an arc $a$ in an oriented graph $\overrightarrow{D}$ is defined analogously, and is denoted $\overrightarrow{D} \setminus a$. The [*converse*]{} of an arc $a= (u,v)$ is the arc $(v,u)$, denoted $a^*$. If we replace an arc $a$ with its converse $a^*$, we obtain an oriented graph with arc set $A(\overrightarrow{D} \setminus a) \cup a^*$ and vertex set $V(\overrightarrow{D})$; we denote the resulting oriented graph $\overrightarrow{D}(a^*)$. We call this replacement [*switching the direction of a*]{}. If we switch the direction of every arc in an oriented graph $\overrightarrow{D}$, we call the 