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...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Published: |
Elsevier
2017
|
| Summary: | 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. |
|---|