Erdos-Ko-Rado theorems for simplicial complexes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Woodroofe, Russ

关键词: Erdos-Ko-Rado;    Algebraic shifting;    Cohen-Macaulay;    Shellable;    Depth;    Independence complex;   

DOI  :  10.1016/j.jcta.2010.11.022

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier Inc. All rights reserved.

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