# Definition:Edge Deletion

## Definition

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 $G - e$.