Year: 2025
Type: preprint
Abstract: We show that if a simplicial complex is a near-cone of sufficiently high depth, then the only maximum families of small pairwise intersecting faces are those with a common intersection. Thus, near-cones of sufficiently high depth satisfy the strict Erdős-Ko-Rado property conjectured by Holroyd and Talbot and by Borg. One consequence is a strict Erdős-Ko-Rado theorem for independence complexes of chordal graphs with an isolated vertex. Under stronger shiftedness conditions, we prove a sharper stability theorem of Hilton-Milner type, as well as two cross-intersecting theorems.
Source: arXiv (Cornell University)
Authors: Bulavka, Denys, Woodroofe, Russ
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416525313
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