  We prove that if $G$ is a 2-connected graph with $\delta(G) \geqslant
\frac{v(G) + 2}{3}$ then $G$ has a cycle $W$ such that $V(G - W)$ is
independent. This result is best possible in the sense that it becomes false if
$\frac{v(G) + 2}{3}$ is replaced by any smaller number.
