“…Thomassen [20] proved that the vertex set of a simple graph G (that is, a graph without multiple edges) with minimum degree at least 12d can be divided into two nonempty sets A, B such that the subgraphs G(A), G(B), induced by A, B, respectively, have minimum degree at least d. Subsequently, Stiebiz [15] proved the conjecture in [20] that the same conclusion holds if the minimum degree of G is at least 2d + 1 (and this is best possible).…”