  In the first few homological gradings, there is an isomorphism between the
Khovanov homology of a link and the categorification of the chromatic
polynomial of a graph related to the link. In this article, we show that the
categorification of the chromatic polynomial only contains torsion of order
two, and hence Khovanov homology only contains torsion of order two in the
gradings where the isomorphism is defined. We also prove that odd Khovanov
homology is torsion-free in its first few homological gradings.
