Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648173 | Discrete Mathematics | 2012 | 15 Pages |
Abstract
A Completely Separating System (CSS) C on [n] is a collection of blocks of [n] such that for any pair of distinct points x,yâ[n], there exist blocks A,BâC such that xâAâB and yâBâA. One possible generalization of CSSs are r-CSSs. Let T be a subset of 2[n], the power set of [n]. A point iâ[n] is called r-separable if for every r-subset Sâ[n]â{i} there exists a block TâT with iâT and with the property that S is disjoint from T. If every point iâ[n] is r-separable, then T is an r-CSS (or r-(n)CSS). Furthermore, if T is a collection of k-blocks, then T is an r-(n,k)CSS. In this paper we offer some general results, analyze especially the case r=2 with the additional condition that kâ¤5, present a construction using Latin squares, and mention some open problems.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Matthias Böhm, Karsten Schölzel,