Name
Abstract | ||
|---|---|---|
A family of sets is union-closed if it contains the union of any two of its elements. Reimer (2003) [16] and Czedli (2009) [2] investigated the average size of an element of a union-closed family consisting of m subsets of a ground set with n elements. We determine the minimum average size precisely, verifying a conjecture of Czedli, Maroti and Schmidt (2009) [3]. As a consequence, the union-closed conjecture holds if m=23.2^n - in this case some element of [n] is in at least half the sets of the family. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jcta.2012.10.005 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
m subsets,union-closed family,minimum average size,average size,n element,union-closed conjecture | Discrete mathematics,Family of sets,Combinatorics,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
120 | 3 | 0097-3165 |
Citations | PageRank | References |
5 | 0.50 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Igor Balla | 1 | 5 | 1.85 |
| Béla Bollobás | 2 | 2696 | 474.16 |
| Tom Eccles | 3 | 17 | 5.77 |