  Tuza famously conjectured in 1981 that in a graph without k+1 edge-disjoint
triangles, it suffices to delete at most 2k edges to obtain a triangle-free
graph. The conjecture holds for graphs with small treewidth or small maximum
average degree, including planar graphs. However, for dense graphs that are
neither cliques nor 4-colorable, only asymptotic results are known. Here, we
confirm the conjecture for threshold graphs, i.e. graphs that are both split
graphs and cographs, and for co-chain graphs with both sides of the same size
divisible by 4.
