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- W2090326703 abstract "An [ n , k , r ]-hypergraph is a hypergraph = ( V , E ) whose vertex set V is partitioned into n k -element sets V 1 , V 2 ,…, V n and for which, for each choice of r indices, 1 ≤ i 1 < i 2 < … < i r ≤ n , there is exactly one edge e ∈ E such that | e ∩ V i | = 1 if i ∈ { i 1 , i 2 .…, i r } and otherwise | e ∩ V i | = 0. An independent transversal of an [ n, k, r ]-hypergraph is a set T = { a 1 , a 2 ,…, a n } ⊆ V such that a i ∈ V i for i = 1, 2, …, n and e ⊈ T for all e ∈ E . The purpose of this note is to estimate f r ( k ), defined as the largest n for which any [ n, k, r ]-hypergraph has an independent transversal. The sharpest results are for r = 2 and for the case when k is small compared to r ." @default.
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- W2090326703 date "1994-09-01" @default.
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- W2090326703 title "Independent Transversals in Sparse Partite Hypergraphs" @default.
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- W2090326703 doi "https://doi.org/10.1017/s0963548300001206" @default.
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