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We prove that the property of containing a $k$-regular subgraph in the randomgraph model $G(n,p)$ has a sharp threshold for $k\ge3$. We also show how to usesimilar methods to obtain an easy prove for the (known fact of) sharpness ofhaving a non empty $k$-core for $k\ge3$.

The Property of Having a $k$-Regular Subgraph Has a Sharp Threshold