Article
Max Cuts in Triangle-free Graphs
arXiv
Document Type
Article
Disciplines
Publication Version
Submitted Manuscript
Publication Date
3-25-2021
Abstract
A well-known conjecture by Erdős states that every triangle-free graph on n vertices can be made bipartite by removing at most n2/25 edges. This conjecture was known for graphs with edge density at least 0.4 and edge density at most 0.172. Here, we will extend the edge density for which this conjecture is true; we prove the conjecture for graphs with edge density at most 0.2486 and for graphs with edge density at least 0.3197. Further, we prove that every triangle-free graph can be made bipartite by removing at most n2/23.5 edges improving the previously best bound of n2/18.
Creative Commons License
Creative Commons Attribution 4.0 International
Copyright Owner
The Authors
Copyright Date
2021
Language
en
File Format
application/pdf
Citation Information
József Balogh, Felix Christian Clemen and Bernard Lidicky. "Max Cuts in Triangle-free Graphs" arXiv (2021) Available at: http://works.bepress.com/bernard-lidicky/71/
This preprint is made available through arXiv: https://arxiv.org/abs/2103.14179.