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arXiv · 2206.14376

A note on the Tuza constant $c_k$ for small $k$

Yun-Shan Lu·Hung-Lung Wang
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Abstract

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 $\tau(H)$. The Tuza constant $c_k$ is defined as $\sup{\tau(H)/ (m+n)}$, where $H$ ranges over all $k$-uniform hypergraphs, with $m$ and $n$ being the number of edges and vertices, respectively. We give an upper bound and a lower bound on $c_k$. The upper bound improves the known ones for $k\geq 7$, and the lower bound improves the known ones for $k\in\{7, 8, 10, 11, 13, 14, 17\}$.

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Yun-Shan Lu, Hung-Lung Wang. 2022-06-29. A note on the Tuza constant $c_k$ for small $k$. https://doi.org/10.1016/j.disc.2023.113756

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