On the number of edges in a graph with no $(k+1)$-connected subgraphs

Anton Bernshteyn, Alexandr Kostochka

Mader proved that for $k\ge 2$ and $n\ge 2k$, every $n$-vertex graph with no $(k+1)$-connected subgraphs has at most $(1+\frac{1}{\sqrt{2}})k(n-k)$ edges. He also conjectured tha…