For each graph, we construct a bigraded chain complex whose graded Euler characteristic is a version of the Tutte polynomial. This work is motivated by earlier work of Khovanov, Helme-Guizon and Rong, and others.
"A categorification for the Tutte polynomial." Algebr. Geom. Topol. 6 (5) 2031 - 2049, 2006. https://doi.org/10.2140/agt.2006.6.2031