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 O-sequence.

Keywords
matroid, $\mathcal{O}$-sequence, multicomplex, ear-decomposition
Mathematical Subject Classification 2010
Primary: 05E40, 05E45
Secondary: 05C75
Milestones
Received: 29 June 2013
Revised: 7 October 2013
Accepted: 23 December 2013
Published: 20 October 2014

Communicated by Kenneth S. Berenhaut
Authors
Nima Imani
Department of Mathematics
University of Washington
Box 354350
Seattle, WA 98195
United States
Lee Johnson
Department of Mathematics
Seattle University
901 12th Avenue
Seattle, WA 98122
United States
Mckenzie Keeling-Garcia
Department of Mathematics
Seattle University
901 12th Avenue
Seattle, WA 98122
United States
Steven Klee
Department of Mathematics
Seattle University
901 12th Avenue
Seattle, WA 98122
United States
Casey Pinckney
Department of Mathematics
Seattle University
901 12th Avenue
Seattle, WA 98122
United States