## Abstract The Erdős‐Sós Conjecture is that a finite graph __G__ with average degree greater than __k__ − 2 contains every tree with __k__ vertices. Theorem 1 is a special case: every __k__‐vertex tree of diameter four can be embedded in __G__. A more technical result, Theorem 2, is obtained by ex
✦ LIBER ✦
On the Erdős-diameter of sets
✍ Scribed by Peter Brass
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 224 KB
- Volume
- 150
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
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## Abstract Let ${\cal F}$ be a __k__‐uniform hypergraph on __n__ vertices. Suppose that $|F\_{1}\cap \cdots \cap F\_{r}|\ge t$ holds for all $F\_{1},\ldots ,F\_{r}\in {\cal F}$. We prove that the size of ${\cal F}$ is at most ${{n-t}\choose {k-t}}$ if $p= {k \over n}$ satisfies and __n__ is suffi