Year: 2026
Type: article
Abstract: We prove that the maximum size of a family of k-element subsets of the set [n] = {1, 2, . . .n} which contains no singleton intersection is n-2 k-2 when 3k -3 ≤ n ≤ k 2 -k + 1.This improves upon a recent result of Cherkashin [Discrete Math.Lett.14 (2024) 85-88].Our proof uses Schrijver's variant of the Lov ász number and furnishes an infinite family of graphs where the Schrijver variant of the Lov ász number is strictly smaller than the Lov ász number.As a consequence of our result and a recent result of Keller and Lifshitz [Adv.Math.392 (2021) #107991], it follows that for k sufficiently large, the maximum size of a k-uniform family on [n] containing no singleton intersection is n-2 k-2 for all n ≥ 3k -3, which is the best possible threshold.
Source: Discrete Mathematics Letters
Author: William Linz
Institution: University of South Carolina
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7154484026
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