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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.)
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References:
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