@inbook{bd99645ca5184f10843fe7655f972fe2,

title = "Max Cuts in Triangle-Free Graphs",

abstract = "A well-known conjecture by Erd{\H o}s 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.",

keywords = "Extremal combinatorics, Graph theory, Triangle-free graphs",

author = "J{\'o}zsef Balogh and Clemen, {Felix Christian} and Bernard Lidick{\'y}",

note = "Funding Information: Acknowledgement. We thank Humberto Naves, Florian Pfender, and Jan Volec for fruitful discussions in early stages of this project. The first author is supported by NSF grants DMS-1764123, DMS-1937241, the Langan Scholar Fund (UIUC), and the Simons Fellowship. The first and second authors are supported by the Arnold O. Beckman Research Award (UIUC RB 18132). The last author is supported by NSF grant DMS-1855653. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-83823-2_82",

language = "English (US)",

series = "Trends in Mathematics",

publisher = "Springer",

pages = "509--514",

booktitle = "Trends in Mathematics",

address = "Germany",

}