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.

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Received November 17, 1999

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

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

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

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Rautenbach, D., Reed, B. The Erdős–Pósa Property for Odd Cycles in Highly Connected Graphs. Combinatorica 21, 267–278 (2001). https://doi.org/10.1007/s004930100024

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