A reduction of proposittional tautologihood to graph-coloring in three colors

Given a disjunctive normal form $A$ of the length $l$ graph $\Gamma_A$ is constructed such that the number of $\Gamma_A$ is $c\cdot l$ and $\Gamma_A$ has a coloring of vert exes in three colors if and only if $A$ is not a tautology.