Strict Erdős-Ko-Rado theorems for simplicial complexes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911031166500864 |
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| author | Bulavka, Denys Woodroofe, Russ |
| author_facet | Bulavka, Denys Woodroofe, Russ |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_15608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strict Erdős-Ko-Rado theorems for simplicial complexes Bulavka, Denys Woodroofe, Russ Combinatorics 05D05, 05E45 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. |
| title | Strict Erdős-Ko-Rado theorems for simplicial complexes |
| topic | Combinatorics 05D05, 05E45 |
| url | https://arxiv.org/abs/2503.15608 |