The $h$-vectors of PS ear-decomposable graphs

Abstract

We consider a family of simple graphs known as PS ear-decomposable graphs. These graphs are one-dimensional specializations of the more general class of PS ear-decomposable simplicial complexes, which were by Chari as a means of understanding matroid simplicial complexes. We outline a shifting algorithm for PS ear-decomposable graphs that allows us to explicitly show that the $h$-vector of a PS ear-decomposable graph is a pure $\mathcal{O}$-sequence.