Year: 2025
Type: article
Abstract: Let $$n > 2k \geq 4$$ n > 2 k ≥ 4 and let $$\mathcal F \subset {[n]\choose k}$$ F ⊂ [ n ] k be an intersecting $$k$$ k -graph on $$n$$ n vertices, that is, $$F\cap F' \neq \emptyset$$ F ∩ F ′ ≠ ∅ for all $$F, F' \in \mathcal F$$ F , F ′ ∈ F . By the Erd\H{o}s--Ko--Rado Theorem $$|\mathcal F| \leq { n - 1\choose k - 1}$$ | F | ≤ n - 1 k - 1 with equality holding only for the full-star, $$\mathcal S_x$$ S x , the family of all $$k$$ k -sets containing the vertex $$x$$ x . If we exclude stars, that is, subfamilies of $$\mathcal S_x$$ S x then $$|\mathcal F| \leq { n - 1\choose k - 1} - { n - k - 1\choose k - 1} + 1$$ | F | ≤ n - 1 k - 1 - n - k - 1 k - 1
Author: P. Frankl
Institution: HUN-REN Alfréd Rényi Institute of Mathematics
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7128427915