A note on the Tuza constant c_k for small k

06/29/2022

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by   Yun-Shan Lu, et al.

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For a hypergraph H, the transversal is a subset of vertices whose intersection with every edge is nonempty. The cardinality of a minimum transversal is the transversal number of H, denoted by τ(H). The Tuza constant c_k is defined as supτ(H)/ (m+n), where H ranges over all k-uniform hypergrpahs, with m and n being the number of edges and vertices, respectively. We give upper and lower bounds on c_k, for 7≤ k≤ 17.