  In \cite{10.2140/agt.2005.5.1365}, Rong and Helme-Guizon defined a
categorification for the chromatic polynomial $P_G(x)$ of graphs $G$, i.e. a
homology theory $H^*(G)$ whose Euler characteristic equals $P_G(x)$. In this
paper, we showed that the rational homoology $H^*(G;\mathbb{Q})$ is supported
in two lines, and develop an analogy of Lee's theory for Khovanov homology. In
particular, we develop a new homology theory $H_{Lee}(G)$, and showed that
there is a spectral sequence whose $E_2$ -term is isomorphic to $H^*(G)$
converges to $H_{Lee}(G)$.
