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A graph $H = \struct {\map V H, \map E H}$ is called a subgraph of a graph $G = \struct {\map V G, \map E G}$ if and only if $\map V H \subseteq \map V G$ and $\map E H \subseteq \map E G$.

That is to say, it contains no vertices or edges that are not in the original graph.

If $H$ is a subgraph of $G$, then:

$G$ contains $H$;
$H$ is contained in $G$


If a graph $F$ is isomorphic to a subgraph $H$ of $G$, then $F$ can be embedded in $G$.