Campus Units
Mathematics
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
9-2017
Journal or Book Title
Journal of Combinatorial Theory, Series B
Volume
126
First Page
83
Last Page
113
DOI
10.1016/j.jctb.2017.04.002
Abstract
Erdős and Sós proposed the problem of determining the maximum number F(n) of rainbow triangles in 3-edge-colored complete graphs on n vertices. They conjectured that F(n) = F(a) + F(b) + F(c) + F(d) + abc + abd + acd + bcd, where a + b + c + d = n and a, b, c, d are as equal as possible. We prove that the conjectured recurrence holds for sufficiently large n. We also prove the conjecture for n = 4k for all k ≥ 0. These results imply that lim F(n)/((n)(3)) = 0.4, and determine the unique limit object. In the proof we use flag algebras combined with stability arguments.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Copyright Owner
Elsevier Inc.
Copyright Date
2017
Language
en
File Format
application/pdf
Recommended Citation
Balogh, József; Hu, Ping; Lidicky, Bernard; Pfender, Florian; Volec, Jan; and Young, Michael, "Rainbow triangles in three-colored graphs" (2017). Mathematics Publications. 125.
https://lib.dr.iastate.edu/math_pubs/125
Comments
This is a manuscript of an article published as Balogh, József, Ping Hu, Bernard Lidický, Florian Pfender, Jan Volec, and Michael Young. "Rainbow triangles in three-colored graphs." Journal of Combinatorial Theory, Series B (2017): 83-113. doi: 10.1016/j.jctb.2017.04.002. Posted with permission.