A New Upper Bound on Extremal Number of Even Cycles
In this paper, we prove $\mathrm{ex}(n, C_{2k})\le (16\sqrt{5}\sqrt{k\log k} + o(1))\cdot n^{1+1/k}$. This improves on a result of Bukh and Jiang from 2017, thereby reducing the best known upper bound by a factor of $\sqrt{5\log k}$.
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| Veröffentlicht in: | The Electronic journal of combinatorics 2021-06, Vol.28 (2) |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we prove $\mathrm{ex}(n, C_{2k})\le (16\sqrt{5}\sqrt{k\log k} + o(1))\cdot n^{1+1/k}$. This improves on a result of Bukh and Jiang from 2017, thereby reducing the best known upper bound by a factor of $\sqrt{5\log k}$. |
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| ISSN: | 1077-8926 1077-8926 |
| DOI: | 10.37236/9861 |