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

Dedicated to the memory of Paul Erdős

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.

This is a preview of subscription content, access via your institution.

Author information



Additional information

Received November 17, 1999


ID="*" This work was supported by a post-doctoral DONET grant.


ID="†" This work was supported by an NSF-CNRS collaborative research grant.


ID="‡" This work was performed while both authors were visiting the LIRMM, Université de Montpellier II, France.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Rautenbach, D., Reed, B. The Erdős–Pósa Property for Odd Cycles in Highly Connected Graphs. Combinatorica 21, 267–278 (2001).

Download citation

  • AMS Subject Classification (2000) Classes:  05C40, 05C70, 05C99