How do you produce a CNF from a circular graph with colouring?
The easiest way is to solve the more general problem for (undirected) graphs and an arbitrary number of colors. Given a graph $G = (V,E)$ and a set of colors $C$, the formula has variables $x(v,c)$ for every vertex $v \in V$ and every color $c \in C$. There are clauses of three kinds:


For each vertex $v$, there is a clause $\bigvee_{c \in C} x(v,c)$.
For each vertex $v$ and each pair of colors $c,d \in C$, there is a clause $\lnot x(v,c) \lor \lnot x(v,d)$.
For each edge $(v,w)$ and each color $c$, there is a clause $\lnot x(v,c) \lor \lnot x(w,c)$.


In words, these clauses state that:


Vertex $v$ gets some color.
Vertex $v$ gets at most one color.
Vertices $v,w$ (which are connected) don't get the same color.