Transversal numbers of uniform hypergraphs

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Abstract

The transversal number τ(H) of a hypergraph H is the minimum cardinality of a set of vertices that intersects all edges of H. For k ≥ 1 define ck =sup τ(H)/(m + n), where H ranges over all k-uniform hypergraphs with n vertices and m edges. Applying probabilistic arguments we show that ck = (1 +o(1))logek/k. This settles a problem of Tuza.

Original languageEnglish
Pages (from-to)1-4
Number of pages4
JournalGraphs and Combinatorics
Volume6
Issue number1
DOIs
StatePublished - Mar 1990

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