论文标题
关于本地密集着色的不可避免的图案的注释
A note on unavoidable patterns in locally dense colourings
论文作者
论文摘要
我们表明，有一个常数$ c $，以至于每$ \ varepsilon> 0 $ 2 $ 2 $颜色的$ k_n $，至少至少$ n/4+\ varepsilon n $两种颜色的n $包含一个完整的子图，其中包含$ 2T $ Vertices的完整子图，其中一个颜色类别a $ k_ a $ k_ a $ k_ {$ k_ { \ varepsilon^{ - ct} $。另外，我们证明，如果$ k_n $是$ 2 $颜色的，最低度至少两种颜色的$ \ varepsilon n $，那么它必须包含完整图的两种自然色彩之一。这两种结果都达到了$ C $的价值，他们回答了Kamčev和Müyesser最近提出的两个问题。
We show that there is a constant $C$ such that for every $\varepsilon>0$ any $2$-coloured $K_n$ with minimum degree at least $n/4+\varepsilon n$ in both colours contains a complete subgraph on $2t$ vertices where one colour class forms a $K_{t,t}$, provided that $n\geq \varepsilon^{-Ct}$. Also, we prove that if $K_n$ is $2$-coloured with minimum degree at least $\varepsilon n$ in both colours then it must contain one of two natural colourings of a complete graph. Both results are tight up to the value of $C$ and they answer two recent questions posed by Kamčev and Müyesser.
