On the homology theory for the chromatic polynomials

Abstract

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 $H^{\ast }(G)$ whose Euler characteristic equals $P_G(x)$. In this paper, we showed that the rational homoology $H^{\ast }(G;\mathbb{Q})$ 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 $H^{\ast }(G)$ converges to $H_{Lee}(G)$.

The main result of the paper is wrong. And the right version has appeared in an earlier paper

References in corpus (1)

• The Jones polynomial and graphs on surfaces

Cited by in corpus (1)

• Multipath cohomology of directed graphs