Erdos-Ko-Rado theorems for simplicial complexes

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.

14 pages; v2 has minor changes; v3 has further minor changes for publication

References in corpus (3)

• Vertex decomposable graphs and obstructions to shellability
• Erdös-Ko-Rado theorems for chordal and bipartite graphs
• Graphs with the Erdos-Ko-Rado property

Cited by in corpus (7)

• The EKR property for flag pure simplicial complexes without boundary
• Betti diagrams from graphs
• On the Hilton-Spencer intersection theorems for unions of cycles
• On $r$-cross $t$-intersecting families for weak compositions
• Chains of modular elements and shellability
• Intersecting families, signed sets, and injection
• An algebraic groups perspective on Erdős-Ko-Rado