Let G be a simple graph with n vertices. The coloring complex ∆(G) was defined by Steingrı́msson, and the homology of ∆(G) was shown to be nonzero only in dimension n − 3 by Jonsson. Hanlon recently showed that the Eulerian idempotents provide a decomposition of the homology group Hn−3(∆(G)) where the dimension of the j component in the decomposition, H n−3(∆(G)), equals the absolute value of th...