Erdos-Ko-Rado theorems for simplicial complexes
Combinatorics
2011-01-27 v3
Abstract
A recent framework for generalizing the Erdos-Ko-Rado Theorem, due to Holroyd, Spencer, and Talbot, defines the Erdos-Ko-Rado property for a graph in terms of the graph's independent sets. Since the family of all independent sets of a graph forms a simplicial complex, it is natural to further generalize the Erdos-Ko-Rado property to an arbitrary simplicial complex. An advantage of working in simplicial complexes is the availability of algebraic shifting, a powerful shifting (compression) technique, which we use to verify a conjecture of Holroyd and Talbot in the case of sequentially Cohen-Macaulay near-cones.
Cite
@article{arxiv.1001.0313,
title = {Erdos-Ko-Rado theorems for simplicial complexes},
author = {Russ Woodroofe},
journal= {arXiv preprint arXiv:1001.0313},
year = {2011}
}
Comments
14 pages; v2 has minor changes; v3 has further minor changes for publication