Induced Cycles in Graphs.

The maximum number vertices of a graph G inducing a 2-regular subgraph of G is denoted by $$c_\mathrm{ind}(G)$$ . We prove that if G is an r-regular graph of order n, then $$c_\mathrm{ind}(G) \ge \frac{n}{2(r-1)} + \frac{1}{(r-1)(r-2)}$$ and we prove that if G is a cubic, claw-free graph on order n, then $$c_\mathrm{ind}(G) > \frac{13}{20}n$$ and this bound is asymptotically best possible. [ABSTRACT FROM AUTHOR]