Lower bound for the induced cycles vertex number in cubic graphs

Prove that every cubic graph G of order n satisfies c_ind(G) >= n/2, thereby establishing the conjectured lower bound for the induced cycles vertex number of cubic graphs.

Background

For a graph G, c_ind(G) is the largest cardinality of a vertex set inducing a 2-regular subgraph. Henning, Joos, Löwenstein, and Sasse established the general lower bound c_ind(G) >= (n+2)/4 for cubic graphs, while conjecturing that the bound can be doubled to n/2.

The paper constructs counterexamples to two conjectures relating c_ind(G) to the (1,2)-domination number, but explicitly notes that these examples do not challenge the stronger lower-bound conjecture c_ind(G) >= n/2. The conjecture remains unresolved in the class of all cubic graphs.