title: reduce vertex cover to hamiltonian cycle why the widget has 12 nodes
body: <p>I know how to prove the hamiltonian cycle is NPC reducing from the vertex cover problem like <a href="http://cs.indstate.edu/%7Ebdhome/HamCycle.pdf" rel="nofollow noreferrer">http://cs.indstate.edu/~bdhome/HamCycle.pdf</a> proved. But I have no idea why the widget we designed should have 12 nodes. I think we can use 4-nodes-widget to replace 12-nodes-widget.
  <a href="https://i.stack.imgur.com/1ReHJ.jpg" rel="nofollow noreferrer">enter image description here</a></p>