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On the choice number of packings. (English) Zbl 1258.05038
Summary: In this note, we show that for positive integers $$s$$ and $$k$$, there is a function $$D(s,k)$$ such that every $$t$$-$$(v,k,\lambda)$$ packing with at least $$D(s,k)\lambda ^{k-t}s^{t-2} v \binom{v-2}{t-2}/\binom{k-2}{t-2}$$ edges, $$2 \leq t \leq k-1$$, has choice number greater than $$s$$.
Consequently, for integers $$s$$, $$k$$, $$t$$, and $$\lambda$$ there is a $$v_{0}(s,k,t,\lambda)$$ such that every $$t$$-$$(v,k,\lambda)$$ design with $$v > v_{0}(s,k,t,\lambda)$$ has choice number greater than $$s$$.
##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C65 Hypergraphs 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
##### Keywords:
hypergraph; $$t$$-design; choice number; packing
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##### References:
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