Set Systems Containing No Singleton Intersection and the Delsarte Number

We prove that the maximum size of a family of k-element subsets of the setThis improves upon a recent result of Cherkashin Discrete Math.Lett.14 (2024) 85-88.Our proof uses Schrijver's variant of the Lov sz number and furnishes an infinite family of graphs where the Schrijver variant of the Lov sz number is strictly smaller than the Lov sz 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.