Let $G$ be a finite simple undirected graph. Suppose there exist subgraphs $G_1,G_2,\dots,G_n$ of $G$, such that $G_i$ and $G_j$, have no common edges and have at most two common vertices, for each $i\neq j$. Is it true that the genus of $G$ is greater than or equal to the sum of genera of each subgraphs $G_i$?

Note: If they have at most one common vertices, then the result hold( using this http://projecteuclid.org/download/pdf_1/euclid.bams/1183524922 paper). Thanks.