Towards a conjecture of Birmelé-Bondy-Reed on the Erdős-Pósa property of long cycles

Jie Ma, Chunlei Zu

A conjecture of Birmelé, Bondy and Reed states that for any integer $\ell \ge 3$, every graph $G$ without two vertex-disjoint cycles of length at least $\ell$ contains a set of at…