Degenerate Vertex Cuts in Sparse Graphs

Thilo Hartel, Johannes Rauch, Dieter Rautenbach

For a non-negative integer $k$, a vertex cut in a graph is $k$-degenerate if it induces a $k$-degenerate subgraph. We show that a graph of order $n$ at least $2k+2$ without a $k$-d…