Partial covering arrays and a generalized ErdosKoRado property
Abstract
The classical Erd\H osKoRado theorem states that if $k\le\floor{n/2}$ then the largest family of pairwise intersecting $k$subsets of $[n]=\{0,1,...,n\}$ is of size ${{n1}\choose{k1}}$. A family of $k$ subsets satisfying this pairwise intersecting property is called an EKR family. We generalize the EKR property and provide asymptotic lower bounds on the size of the largest family ${\cal A}$ of $k$subsets of $[n]$ that satisfies the following property: For each $A,B,C\in{\cal A}$, each of the four sets $A\cap B\cap C;A\cap B\cap C^C; A\cap B^C\cap C; A^C\cap B\cap C$ are nonempty. This generalized EKR (GEKR) property is motivated, generalizations are suggested, and a comparison is made with fixed weight 3covering arrays. Our techniques are probabilistic.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2005
 arXiv:
 arXiv:math/0512139
 Bibcode:
 2005math.....12139C
 Keywords:

 Mathematics  Combinatorics;
 05Bxx
 EPrint:
 16 pages, 4 figures, 2 tables