Help reducing 3-SAT to 3-COLORING
I believe the goal of this construction is to try to assign true or false to each variable. The color assigned to x will determine whether it's true or false, and there's an edge from x to &not;x to ensure that each variable and its negation get different values. The edge from each variable to R ensures that there are only two possible colors that can be assigned to x, one of which means true and one of which meand false.

Hope this helps!