Asymptotic behavior of the chromatic index for hypergraphs
Journal of Combinatorial Theory Series A
Bibliography of publications by Rudolf Ahlswede
Information Theory, Combinatorics, and Search Theory
| Hi-index | 0.00 |
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.