论文标题
用单色树覆盖$ 3 $ - 边缘色的随机图
Covering $3$-edge-coloured random graphs with monochromatic trees
论文作者
论文摘要
我们研究了确定需要多少个单色树来覆盖边彩随机图的顶点的问题。更确切地说，我们表明，对于$ p \ gg n^{ - 1/6} {（\ ln n）}}^{1/6} $，在任何$ 3 $ - edge-gedy-gedy-gedy-geend-edge-edgoling of togragr $ g（n，p）$中，我们可以找到三个单色树，以使他们的联盟覆盖所有角色。对于三种颜色，这是Bucić，Korándi和Sudakov的结果。
We investigate the problem of determining how many monochromatic trees are necessary to cover the vertices of an edge-coloured random graph. More precisely, we show that for $p\gg n^{-1/6}{(\ln n)}^{1/6}$, in any $3$-edge-colouring of the random graph $G(n,p)$ we can find three monochromatic trees such that their union covers all vertices. This improves, for three colours, a result of Bucić, Korándi and Sudakov.
