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A note on the Turán function of even cycles
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Pikhurko, Oleg (2012) A note on the Turán function of even cycles. Proceedings of the American Mathematical Society, Vol.140 (No.11). pp. 3687-3692. doi:10.1090/S0002-9939-2012-11274-2 ISSN 0002-9939.
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Official URL: http://dx.doi.org/10.1090/S0002-9939-2012-11274-2
Abstract
The Tur´an function ex(n, F) is the maximum number of edges in an F-free graph on n vertices. The question of estimating this function for F = C2k, the cycle of length 2k, is one of the central open questions in this area that goes back to the 1930s. We prove that ex(n,C2k) ≤ (k − 1) n1+1/k + 16(k − 1)n, improving the previously best known general upper bound of Verstra¨ete [Combin. Probab. Computing 9 (2000), 369–373] by a factor 8 + o(1) when n � k.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||
| Publisher: | American Mathematical Society | ||||
| ISSN: | 0002-9939 | ||||
| Official Date: | 2012 | ||||
| Dates: |
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| Volume: | Vol.140 | ||||
| Number: | No.11 | ||||
| Number of Pages: | 6 | ||||
| Page Range: | pp. 3687-3692 | ||||
| DOI: | 10.1090/S0002-9939-2012-11274-2 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | National Science Foundation | ||||
| Grant number: | DMS-0758057 |
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