Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777439 | European Journal of Combinatorics | 2017 | 9 Pages |
Abstract
Two families A and B of k-subsets of an n-set are called cross-intersecting if Aâ©Bâ 0̸ for all AâA,BâB. Strengthening the classical ErdÅs-Ko-Rado theorem, Pyber proved that |A||B|â¤nâ1kâ12 holds for nâ¥2k. In the present paper we sharpen this inequality. We prove that assuming |B|â¥nâ1kâ1+nâikâi+1 for some 3â¤iâ¤k+1 the stronger inequality |A||B|â¤(nâ1kâ1+nâikâi+1)(nâ1kâ1ânâikâ1) holds. These inequalities are best possible. We also present a new short proof of Pyber's inequality and a short computation-free proof of an inequality due to Frankl and Tokushige (1992).
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Peter Frankl, Andrey Kupavskii,