Maximising the number of induced cycles in a graph

摘要

We determine the maximum number of induced cycles that can be contained in a graph on n >= n(0) vertices, and show that there is a unique graph that achieves this maximum. This answers a question of Chvatal 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 >= n(0) vertices and characterise the extremal graphs. This resolves a conjecture of Chvatal and Tuza from 1988. (C) 2017 Elsevier Inc. All rights reserved.