<a href="https://en.wikipedia.org/wiki/Gadget_(computer_science)" class="extiw" title="en:Gadget (computer science)">Gadgets</a> for an <a href="https://en.wikipedia.org/wiki/NP-complete" class="extiw" title="en:NP-complete">NP-completeness</a> proof of <a href="https://en.wikipedia.org/wiki/Graph_coloring" class="extiw" title="en:Graph coloring">graph 3-coloring</a>, by reduction from 3-Satisfiability. The variable and clause gadgets are shown on the upper and lower left, respectively, and the right side of the figure shows the complete reduction for the instance (<i>x</i> ∨ <i>y</i> ∨ ~<i>z</i>) ∧ (~<i>x</i> ∨ ~<i>y</i> ∨ <i>z</i>) with three variables and two clauses. This reduction is from Oded Goldreich, <i>Computational Complexity: A Conceptual Perspective</i>, Cambridge University Press, 2008, Proposition 2.27, p. 81.
<a href="//commons.wikimedia.org/wiki/User:David_Eppstein" class="mw-redirect" title="User:David Eppstein">David Eppstein</a>
<span class="int-own-work" lang="en">Own work</span>