#### Vol. 7, No. 6, 2014

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

### Nima Imani, Lee Johnson, Mckenzie Keeling-Garcia, Steven Klee and Casey Pinckney

Vol. 7 (2014), No. 6, 743–750
##### 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 $\mathsc{O}$-sequence.

##### Keywords
matroid, $\mathcal{O}$-sequence, multicomplex, ear-decomposition
##### Mathematical Subject Classification 2010
Primary: 05E40, 05E45
Secondary: 05C75