# The Erdös-Ko-Rado properties of set systems defined by double partitions

Borg, Peter and Holroyd, Fred (2009). The Erdös-Ko-Rado properties of set systems defined by double partitions. Discrete Mathematics, 309(14) pp. 4754–4761.

## Abstract

Let be a family of subsets of a finite set . The star of at is the sub-family . We denote the sub-family by .
A double partition P of a finite set V is a partition of into 'large sets' that are in turn partitioned into 'small sets'. Given such a partition, the family induced by is the family of subsets of whose intersection with each large set is either contained in just one small set or empty.
Our main result is that, if one of the large sets is trivially partitioned (that is, into just one small set) and is not greater than the least cardinality of any maximal set of , then no intersecting sub-family of is larger than the largest star of . We also characterise the case when every extremal intersecting sub-family of is a star of .

## Metrics

### Public Attention

Altmetrics from Altmetric

### Number of Citations

Citations from Dimensions