The graph \(G_4\) is NOT a subgraph of \(G_1\text{,}\) even though it looks like all we did is remove vertex \(e\text{.}\) The reason is that in \(E_4\) we have the edge \(\{c,f\}\) but this is not an element of \(E_1\text{,}\) so we don't have the required \(E_4 \subseteq E_1\text{.}\)
in-context