Bounding the vertex cover number of a hypergraph
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For a hypergraphH, we denote by
τ(H) the minimumk such that some set ofk vertices meets all the edges,
ν(H) the maximumk such that somek edges are pairwise disjoint, and
λ(H) the maximumk≥2 such that the incidence matrix ofH has as a submatrix the transpose of the incidence matrix of the complete graphK k .
We show that τ(H) is bounded above by a function of ν(H) and λ(H), and indeed that if λ(H) is bounded by a constant then τ(H) is at most a polynomial function of ν(H).
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- Bounding the vertex cover number of a hypergraph
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