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arXiv · 1603.02960

Maximising the number of induced cycles in a graph

Natasha Morrison·Alex Scott
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Abstract

We determine the maximum number of induced cycles that can be contained in a graph on $n\ge n_0$ vertices, and show that there is a unique graph that achieves this maximum. This answers a question of Tuza. We also determine the maximum number of odd or even cycles that can be contained in a graph on $n\ge n_0$ vertices and characterise the extremal graphs. This resolves a conjecture of Chvátal and Tuza from 1988.

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Natasha Morrison, Alex Scott. 2017-04-12. Maximising the number of induced cycles in a graph. https://arxiv.org/abs/1603.02960

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