论文标题
红蓝色图中的单色三角包装
Monochromatic triangle packings in red-blue graphs
论文作者
论文摘要
我们证明，在$ k_n $的每$ 2 $ edge上，都有$ n^2/12 + o（n^2）$ edge-dise-disshot-dishoint单色三角形的集合，从而证实了erdős的猜想。我们还证明了相应的稳定性结果，这表明接近上述绑定的$ 2 $颜色具有接近两分的颜色类。作为证明的一部分，我们确认了Tyomkyn最近对该问题的分数版本的猜想。
We prove that in every $2$-edge-colouring of $K_n$ there is a collection of $n^2/12 + o(n^2)$ edge-disjoint monochromatic triangles, thus confirming a conjecture of Erdős. We also prove a corresponding stability result, showing that $2$-colourings that are close to attaining the aforementioned bound have a colour class which is close to bipartite. As part of our proof, we confirm a recent conjecture of Tyomkyn about the fractional version of this problem.
