Let $G = (V, E)$ be a graph. Assume that $G$ is bipartite, connected, and each vertex of $G$ has degree $2016$. Let $v \in V$ and $H = (V - v, E - \{e \in E: v \in e\}).$ Show that the graph $H$ is connected.
I think it's a little bit complicated. It would be helpful to count up vertices in $G$.