A multicomplex of partially edge-rooted forests

Abstract

A coned graph View the MathML source 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 View the MathML source 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.