Maximising the number of induced cycles in a graph

We determine the maximum number of induced cycles that can be contained in a graph on n≥n0 vertices, and show that there is a unique graph that achieves this maximum. This answers a question of Chvátal and Tuza from the 1980s. We also determine the maximum number of odd or even induced cycles that can be contained in a graph on n≥n0 vertices and characterise the extremal graphs. This resolves a conjecture of Chvátal and Tuza from 1988.