A short proof of the Hilton-Milner Theorem
Denys Bulavka, Russ Woodroofe
Abstract
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
Table of Contents
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A short proof of the Hilton-Milner Theorem
Authors
Abstract
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
Paper Structure
This paper contains 7 sections, 5 theorems, 5 equations.
Table of Contents
Key Result
Theorem 1
Let $k\leq n/2$. If $\mathcal{F}$ is a family of pairwise-intersecting $k$-element subsets of $[n]$, where $\bigcap_{F\in\mathcal{F}}F=\emptyset$, then $\left|\mathcal{F}\right|\leq{n-1 \choose k-1}-{n-1-k \choose k-1}+1$.
Theorems & Definitions (10)
- Theorem 1: Hilton and Milner 1967 Hilton/Milner:1967
- Theorem 2
- proof
- Lemma 3: essentially Frankl and Füredi Frankl/Furedi:1986
- proof
- Remark 4
- proof
- Theorem 5
- Lemma 6
- proof : Proof.