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We study optimal minimum degree conditions when an $n$-vertex graph $G$contains an $r$-regular $r$-connected subgraph. We prove for $r$ fixed and $n$large the condition to be $\delta(G) \ge \frac{n+r-2}{2}$ when $nr \equiv 0\pmod 2$. This answers a question of M.~Kriesell.

Minimum degree conditions for containing an $r$-regular $r$-connected subgraph