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- Title
Towards a conjecture of Birmelé–Bondy–Reed on the Erdős–Pósa property of long cycles.
- Authors
Jie Ma; Chunlei Zu
- Abstract
A conjecture of Birmelé, Bondy, and Reed states that for any integer ℓ ≥ 3, every graph G without two vertex‐disjoint cycles of length at least ℓ contains a set of at most ℓ vertices which meets all cycles of length at least ℓ. They showed the existence of such a set of at most 2ℓ + 3 vertices. This was improved by Meierling, Rautenbach, and Sasse to 5ℓ∕ ∕ 3 + 29/2. Here we present a proof showing that at most 3ℓ∕ ∕ 2+7/2 vertices suffice.
- Subjects
LOGICAL prediction; INTEGERS; RAMSEY numbers; REED-Muller codes
- Publication
Journal of Graph Theory, 2023, Vol 103, Issue 1, p148
- ISSN
0364-9024
- Publication type
Article
- DOI
10.1002/jgt.22911