W6jcik, P., Density of union-closed families, Discrete Mathematics 105 (1992) 259-267. Two theorems related to Frankl's conjecture about union-closed families are proved. The first one states how small the sum of degrees in an m-element set may be. Our second result deals with the smallest densities
Union-closed families of sets
✍ Scribed by Piotr Wójcik
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 532 KB
- Volume
- 199
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
We use a lower bound on the number of small sets in an idea1 to show that for each unionclosed family of n sets there exists an element which belongs to at least of them, provided n is large enough.
📜 SIMILAR VOLUMES
A union closed family A is a finite family of sets such that the union of any two sets in A is also in A. The conjecture under consideration is Conjecture 1: For every union closed family A, there exists some x contained in at least half the members of A. We study the structure of such families (as
## Abstract It is well known that in Bishop‐style constructive mathematics, the closure of the union of two subsets of ℝ is ‘not’ the union of their closures. The dual situation, involving the complement of the closure of the union, is investigated constructively, using completeness of the ambient