The Erdős–Pósa Property for Odd Cycles in Highly Connected Graphs

In [9] Thomassen proved that a -connected graph either contains k vertex disjoint odd cycles or an odd cycle cover containing at most 2k-2 vertices, i.e. he showed that the Erdős–Pósa property holds for odd cycles in highly connected graphs. In this paper, we will show that the above statement is still valid for 576k-connected graphs which is essentially best possible.