A NOTE ON THE TURAN FUNCTION OF EVEN CYCLES

被引：37

作者：

Pikhurko, Oleg ^{[1
]}

机构：

[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 140卷 / 11期

基金：

美国国家科学基金会;

关键词：

GRAPHS; NUMBER;

D O I：

10.1090/s0002-9939-2012-11274-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Turan 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 = C-2k, 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, C-2k) <= (k - 1)n(1+1/k) + 16(k - 1)n, improving the previously best known general upper bound of Verstraete [Combin. Probab. Computing 9 (2000), 369-373] by a factor 8 + o(1) when n >> k.

引用

页码：3687 / 3692

页数：6

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