A multicomplex of partially edge-rooted forests

A coned graph G ˆ is the union of a finite graph G and a star on its vertices. In this paper, we show that the h -vector of the cycle matroid of G ˆ is the f -vector of a pure multicomplex constructed from the partially edge-rooted forests in G . This result proves a conjecture by Stanley (1996) [6] in the case of the cycle matroid of coned graphs.