I have an example for a reduction of 3CNF to Clique, there is one thing I don't get about it, hopefully you could clarify it. The reduction works like this:
Construct a graph G = (V, E) as follows:
Vertices: Each literal corresponds to a vertex.
Edges: All vertices are connected with an edge except the vertices of the same clause and vertices with negated literals.
Why is it important that that negated literals will not be connected? How would that effect the reduction?