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Union-closed families of sets

✍ Scribed by Balla, Igor; Bollobás, Béla; Eccles, Tom

Book ID
120296979
Publisher
Elsevier Science
Year
2013
Tongue
English
Weight
245 KB
Volume
120
Category
Article
ISSN
0097-3165

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📜 SIMILAR VOLUMES

Union-closed families of sets
Union-closed families of sets
✍ Piotr Wójcik 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 532 KB

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.

Union-closed families
Union-closed families
✍ Bjorn Poonen 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 784 KB
Density of union-closed families
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
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
On Union-Closed Families, I
✍ Robert T. Johnson; Theresa P. Vaughan 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 93 KB