The Erdös-Ko-Rado theorem states that if F is a family of k-subsets of an n-set no two of which are disjoint, n ≥ 2k, then |F| ≤ n-1 k-1 holds. Taking all k-subsets through a point shows that this bound is best possible. Hilton and Milner showed that if ∩ F = Ø then |F|≤ n-1 k-1- n-k-1 k-1+1 holds and this is best possible. In this note a new, short proof of this theorem is given.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics