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

Abstract

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