Name
Abstract | ||
|---|---|---|
Let $\cal{B}(n, \leq 4)$ denote the subsets of $[n]:=\{ 1, 2, \dots, n\}$ of at most 4 elements. Suppose that $\cal{F}$ is a set system with the property that every member of $\cal{B}$ can be written as a union of (at most) two members of $\cal{F}$. (Such an $\cal{F}$ is called a 2-base of $\cal{B}$.) Here we answer a question of Erdös proving that \[|\FF|\geq 1+n+\binom{n}{2}- \Bigl\lfloor \frac{4}{3}n\Bigr\rfloor\], and this bound is best possible for $n\geq 8$. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1017/S0963548305007248 | Combinatorics, Probability & Computing |
Keywords | Field | DocType |
set system | Discrete mathematics,Combinatorics,Mathematics | Journal |
Volume | Issue | ISSN |
15 | 1-2 | 0963-5483 |
Citations | PageRank | References |
4 | 0.69 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zoltán Füredi | 1 | 1237 | 233.60 |
| Gyula O. H. Katona | 2 | 264 | 66.44 |