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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


Density of union-closed families
✍ Piotr Wójcik 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 425 KB

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

On Union-Closed Families, I
✍ Robert T. Johnson; Theresa P. Vaughan 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 174 KB

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

On Union-Closed Families, I
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Constructive complements of unions of tw
✍ Douglas S. Bridges 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 69 KB

## 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