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We prove that if $G$ is a graph and $r_1, ..., r_k \in \mathbb{Z}_{\geq 0}$such that $\sum_{i=1}^k r_i \geq \Delta(G) + 2 - k$ then $V(G)$ can bepartitioned into sets $V_1, ..., V_k$ such that $\Delta(G[V_i]) \leq r_i$ and$G[V_i]$ contains no non-complete $r_i$-regular components for each $1 \leq i\leq k$. In particular, the vertex set of any graph $G$ can be partitioned into$\left \lceil \frac{\Delta(G) + 2}{3} \right \rceil$ sets, each of whichinduces a disjoint union of triangles and paths.

Destroying Non-Complete Regular Components in Graph Partitions