Name
Abstract | ||
|---|---|---|
An intersecting system of type (∃, ∀, k, n) is a collection 𝔽={ℱ1, ..., ℱm} of pairwise disjoint families of k-subsets of an n-element set satisfying the following condition. For every ordered pair ℱi and ℱj of distinct members of 𝔽 there exists an A∈ℱi that intersects every B∈ℱj. Let In (∃, ∀, k) denote the maximum possible cardinality of an intersecting system of type (∃, ∀, k, n). Ahlswede, Cai and Zhang conjectured that for every k≥1, there exists an n0(k) so that In (∃, ∀, k)=(n−1/k−1) for all nn0(k). Here we show that this is true for k≤3, but false for all k≥8. We also prove some related results. |
Year | DOI | Venue |
|---|---|---|
1997 | 10.1017/S0963548397003003 | Combinatorics, Probability & Computing |
Keywords | DocType | Volume |
related result,distinct member,intersecting system,pairwise disjoint family,following condition,Intersecting Systems,maximum possible cardinality | Journal | 6 |
Issue | Citations | PageRank |
2 | 0 | 0.34 |
References | Authors | |
1 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| R. Ahlswede | 1 | 85 | 11.81 |
| Noga Alon | 2 | 10468 | 1688.16 |
| P. L. Erdös | 3 | 48 | 13.10 |
| M. Ruszinkó | 4 | 230 | 35.16 |
| L. A. Székely | 5 | 113 | 19.81 |