Speaker:  Russ Woodroofe, Washington University
Title:  Chordal clutters and k-decomposability
Time: 2:30 PM, Monday, November 9, 2009
Place:  Malott 206

Abstract:  The family of chordal graphs has excellent properties for geometric combinatorics. Most interesting to us in this talk is that the independence complex of a chordal graph is shellable, and in fact vertex decomposable.

I'll present an extension of the definition of chordal from graphs to clutters. The resulting family of clutters is a common generalization of chordal graphs, circuit clutters of matroids, and "acyclic" clutters. The independence complex of a chordal clutters is shellable. In order to prove shellability we extend the definition of k-decomposable to non-pure complexes. I will also discuss a potential application in obstructions to shellability, as well as other nice properties of chordal graphs that are satisfied by chordal clutters.

November 2, 2009