The regularity method for graphs with few 4‐cycles
Name
2004.10180.pdf
Description
Accepted version
Size
381.7 KB
Format
Adobe PDF
Checksum (MD5)
49f09e63c20726d8dcb5100910d4eef3
Author(s)
Conlon, David
Fox, Jacob
Sudakov, Benny
Zhao, Yufei
Date Issued
2021
Journal
Journal of the London Mathematical Society
Publisher
Wiley
Citation
Conlon, David, Fox, Jacob, Sudakov, Benny and Zhao, Yufei. 2021. "The regularity method for graphs with few 4‐cycles." Journal of the London Mathematical Society, 104 (5).
Version
Author's final manuscript
Abstract
We develop a sparse graph regularity method that applies to graphs with few
4-cycles, including new counting and removal lemmas for 5-cycles in such
graphs. Some applications include:
* Every $n$-vertex graph with no 5-cycle can be made triangle-free by
deleting $o(n^{3/2})$ edges.
* For $r \geq 3$, every $n$-vertex $r$-graph with girth greater than $5$ has
$o(n^{3/2})$ edges.
* Every subset of $[n]$ without a nontrivial solution to the equation $x_1 +
x_2 + 2x_3 = x_4 + 3x_5$ has size $o(\sqrt{n})$.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1112/JLMS.12500
