Year: 2009
Type: article
Abstract: Inspired by several recent papers on the edge ideal of a graph $G$, we study the equivalent notion of the independence complex of $G$. Using the tool of vertex decomposability from geometric combinatorics, we show that $5$-chordal graphs with no chordless $4$-cycles are shellable and sequentially Cohen-Macaulay. We use this result to characterize the obstructions to shellability in flag complexes, extending work of Billera, Myers, and Wachs. We also show how vertex decomposability may be used to show that certain graph constructions preserve shellability.
Author: Russ Woodroofe
Institution: Washington University in St. Louis
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W2095895362