2018年11月17日 |  English version
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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: 20181110日(周六)10:00

报告地点:  行健楼学术报告厅526

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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