After fiddling around some more you come across another vari

After fiddling around some more you come across another variant that uses only four additional vertices (u1, u2, u3, and u4) per clause. Here is the gadget for the clause x1 V x3 V x7: Prove that this gadget does not work by showing that some times it is not possible to 3-color the gadget when the literals are colored T or F and at least one of them is colored T.

Solution