Figure 2

(a) The variable gadget for variable x with literal vertices x¹, x² and ¬ x , as well as the four auxiliary vertices x ', x '', x ''', x '''' that do not appear in any other hyperedge of$H_{\varphi }$. (b) 2-clause gadget with literal vertices p and q, as well as the two auxiliary vertices c and c' that do not appear in any other hyperedge of H _ϕ . (c) 3-clause gadget with literal vertices p, q and r.