# Graph Theory: decide if there are two sets of vertices \$ V_1 \$ and \$ V_2 \$ (\$ V_1 + V_2 = V \$) so that both \$ V_1 \$ and \$ V_2 \$ are the vertex cover

Given a graph $$G$$ and its set of vertices $$V$$. Taking into account the following problem:

there are two sets of separate vertices $$V_1$$ Y $$V_2$$ ( $$V_1 cup V_2 = V$$) such that both $$V_1$$ Y $$V_2$$ they are covered with vertices of $$G$$?

I wonder if the previous decision problem is difficult.

We can probably ask continuously "is there a vertex-size cover? $$k$$ ($$k = 1,2, …, | V |$$)? "Suppose we find an answer $$V_1$$ of size $$k$$. Then we can check if $$V – V_1$$ It is a vertex cover. Does this argument show that the original decision problem is difficult?