2018年11月17日 |  English version

 科学研究
 Rainbow triangles in three-colored graphs
 报告题目: Rainbow triangles in three-colored graphs报告人: 胡平副教授, 中山大学数学院报告时间: 2018年11月10日（周六）10:00报告地点:  行健楼学术报告厅526室邀请人：许宝刚教授Abstract: Erd\H os and S\'os 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 $n = 4^k$ for all $k \geq 0$. These results imply that $\lim \frac{F(n)}{{n\choose 3}}=0.4$, and determine the unique limit object.In the proof we use flag algebras combined with stability arguments.Joint work with J\'{o}zsef Balogh, Bernard Lidick\'{y}, Florian Pfender, Jan Volec and Michael Young.
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