To reduce 3CNF to 3COL, for a given formula F construct the
following graph G:

The vertices of G are all the variables of F, plus their
negations, plus 5 vertices for each clause, and 3 special
vertices: TRUE, FALSE, BLUE.

There are two types of edges:

Type 1: For each variable x:

     BLUE
      /\
     /  \
    /    \
   x-----(-x)

and also a triangle on TRUE, FALSE, BLUE.

Type 2: For every clause (a v b v c) we have the following 
widget:

a------O
       |\
       | O----O
       |/     |\
b------O      | \
              |  \
              |   TRUE
              |  /
              | /
              |/
c-------------O

note that this widget is 3col by TRUE, FALSE, BLUE, iff
exactly one of a,b,c is colored TRUE (ie., the clause is
true).