Let $G$ be a simple undirected graph and $G_1$ and $G_2$ are two subgraphs of $G$, with $E(G_1) \cap E(G_2) =\emptyset$. Which of the following conditions would imply that $G$ is not toroidal:

a; $G_1 \cong K_{3,3}$, $G_2 \cong K_5$, $|V(G_1)\cap V(G_2)| \leq 2$.

b; $G_1, G_2 \cong K_{3,3}$, $|V(G_1)\cap V(G_2)| \leq 2$.

c; $G_1, G_2 \cong K_{3,3}$, $|V(G_1)\cap V(G_2)| \leq 3$ and $K_{6,3}$ is not a subgraph of $G$.

Thanks in advance.