\begin{definition}[Definition:Edge Deletion]
Let $G = \struct {V, E}$ be an (undirected) graph.
Let $F \subseteq E$ be a set of edges of $G$.
Then the '''graph obtained by deleting $F$ from $G$''', denoted by $G - F$, is the subgraph of $G$ containing the same vertices as $G$ but with all the elements of $F$ removed.
That is:
:$G - F = \struct {V, E \setminus F}$
Informally, $G - F$ is the graph obtained from $G$ by removing all edges in $F$.
If $F$ is a singleton such that $F = \set e$, then $G - F$ may be expressed $G - e$.
\end{definition}