Name
Abstract | ||
|---|---|---|
Three intersection theorems are proved. First, we determine the size of the largest set system, where the system of the pairwise unions is $$l$$l-intersecting. Then we investigate set systems where the union of any $$s$$s sets intersect the union of any $$t$$t sets. The maximal size of such a set system is determined exactly if $$s+t\\le 4$$s+t≤4, and asymptotically if $$s+t\\ge 5$$s+t¿5. Finally, we exactly determine the maximal size of a $$k$$k-uniform set system that has the above described $$(s,t)$$(s,t)-union-intersecting property, for large enough $$n$$n. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s00373-014-1456-7 | Graphs and Combinatorics |
Keywords | Field | DocType |
Extremal set systems, Intersecting family, Erdős-Ko-Rado theorem, $$\Delta $$Δ-system, Forbidden subposets, 05D05 | Discrete mathematics,Pairwise comparison,Combinatorics,Erdős–Ko–Rado theorem,Mathematics,The Intersect | Journal |
Volume | Issue | ISSN |
31 | 5 | 1435-5914 |
Citations | PageRank | References |
2 | 0.43 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gyula O. H. Katona | 1 | 264 | 66.44 |
| Dániel T. Nagy | 2 | 3 | 1.19 |