Lixing Yi

An improved upper bound for Tuza's conjecture via 2-colorable triangle families

Tuza's conjecture states that for any graph $G$, the minimum size of a triangle transversal $\tau(G)$ is at most twice the maximum size of a set of edge-disjoint triangles $\nu(G)$. In this note, we prove $\tau(G) \leq \frac{63}{22}\nu(G)$, improving the previous bound $\tau(G) \leq \frac{66}{23}\nu(G)$ established by...