Journal or Book Title
Journal of Combinatorial Theory, Series B
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.
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Balogh, Jozef; Hu, Ping; Lidicky, Bernard; Pfender, Florian; Volec, Jan; and Young, Michael, "Rainbow triangles in three-colored graphs" (2017). Mathematics Publications. 125.
Available for download on Saturday, September 01, 2018