Separating a Graph into 2 sets with crossing edges only

I’m trying to think of an algorithm that checks the existence of partition $$(V_1,V_2)$$ in undirected $$G$$ where all the edges are crossing edges between $$V_1$$ and $$V_2$$. For example, if $$e=(a,b)$$ then $$a in V_1$$, $$b in V_2$$. Oh and $$V_1+V_2=V$$.

I’ve been thinking to come up with an algorithm but I simply cannot. I’ve checked some previous posts and they weren’t that helpful. Can someone give me a hint?