Cycle packing
Name
Fox_Cycle packing.pdf
Size
221.72 KB
Format
Adobe PDF
Checksum (MD5)
5c7968ad8ce8eff5f0fa7536da1e02b5
Author(s)
Conlon, David
Fox, Jacob
Sudakov, Benny
Date Issued
December 2014
Journal
Random Structures & Algorithms
Publisher
Wiley-VCH Verlag GmbH & Co.
Citation
Conlon, David, Jacob Fox, and Benny Sudakov. “Cycle Packing.” Random Struct. Alg. 45, no. 4 (October 16, 2014): 608–626.
Version
Author's final manuscript
Abstract
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be partitioned into O(n) cycles and edges. They observed that one can easily get an O(nlogn) upper bound by repeatedly removing the edges of the longest cycle. We make the first progress on this problem, showing that O(nloglogn) cycles and edges suffice. We also prove the Erdős-Gallai conjecture for random graphs and for graphs with linear minimum degree.
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/10.1002/rsa.20574
