Résumé
We show that every graph G of maximum degree Δ and sufficiently large order has a vertex cutset S of order at most Δ that induces a subgraph G[S] of maximum degree at most Δ−3. For Δ∈{4,5}, we refine this result by considering also the average degree of G[S]. If G has no Kr,r subgraph, then we show the existence of a vertex cutset that induces a subgraph of maximum degree at most (1−1(r2))Δ+O(1).