  Khovanov introduced a bigraded cohomology theory of links whose graded Euler
characteristic is the Jones polynomial. The theory was subsequently applied to
the chromatic polynomial of graph, resulting in a categorification known as the
``chromatic homology''. Much as in the Khovanov homology, the chromatic
polynomial can be obtained by taking the Euler characteristic of the chromatic
homology. In the present paper, we introduce a combinatorial description of
enhanced states that can be applied to analysis of the homology in an explicit
way by hand. Using the new combinatorial description, we show a splitting
property of the chromatic homology for a certain class of graphs. Finally, as
an application of the description, we compute the chromatic homology of the
complete graph.
