Tuza's Conjecture for Graphs of Maximum Degree at Most 10

Source abstract

For a finite simple graph $G$, let $ν(G)$ be the maximum number of pairwise edge disjoint triangles and $τ(G)$ the minimum number of edges meeting every triangle. Tuza conjectured in 1981 that every such $G$ satisfies $τ(G) \le 2 ν(G).$ We prove the conjecture for the class of graphs with $Δ\le10.$