Let $G$ be a finite simple undirected graph. Suppose there exist subgraph $G_1,G_2,\dots,G_n$ of $G$, such that $E(G_i)\cap E(G_j) = \emptyset$ and $|V(G_i)\cap V(G_j)| \leq 2$, for $i\neq j$. Then, can we conclude that $\gamma(G) \geq \gamma(G_1)+\dots+\gamma(G_n)$?

( $V(G),E(G)$ and $\gamma(G)$ denote the set of vertices, the set of edges and the genus of the graph $G$, respectively)

Thanks in advance.