Author

Si-Chen Wang

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Preprint Sep 2026

A Tight Fractional Version of Generalized Tuza's Conjecture

For an $r$-uniform hypergraph $H$, let $\nu(H)$ be the maximum number of edges no two of which share $r-1$ vertices, and $\tau(H)$ the minimum number of $(r-1)$-sets such that every edge contains one of them. Aharoni and Zerbib conjectured that $\tau(H)\le\lceil\frac{r+1}{2}\rceil\,\nu(H)$, which for $r=3$ generalizes...

Si-Chen Wang · 0 citations

Preprint Sep 2026

A Bound Below 2.8 for Tuza's Conjecture

Let $\nu(G)$ be the maximum number of edge-disjoint triangles in a graph $G$ and $\tau(G)$ the minimum number of edges meeting every triangle. Tuza conjectured that $\tau(G)\le 2\nu(G)$. We prove that $\tau(G)\le (165/59)\nu(G)$. The constant $165/59\approx 2.797$ improves the bound $66/23\approx 2.870$ that Haxell pro...

Si-Chen Wang · 0 citations