On the choice number of packings

Abstract

In this note, we show that for positive integers s and k, there is a function D(s,k) such that every t-(v,k) packing with at least D(s,k) k-t2 t-2vv-2t-2/k-2t-2 edges, 2circk-1, has choice number greater than s. Consequently, for integers s, k, t, and there is a v0(s,k,t) such that every t-(v,k) design with v>v0(s,k,t) has choice number greater than s. © 2012 Wiley Periodicals, Inc.