论文标题
三重系统中具有多种颜色的集团
Cliques with many colors in triple systems
论文作者
论文摘要
Erds和Hajnal构建了4色的$ n $ element套件的四色，使每个$ n $ element子集包含2个带有不同颜色的三元组，而$ n $在$ n $中是双重指数的。 Conlon，Fox和Rödl询问是否有一些整数$ Q \ ge 3 $和$ Q $ - $ n $ element套件的三元组颜色，以使每个$ n $ element子集都具有3个具有不同颜色的三倍，而$ n $是$ n $ in $ n $ in $ n $。我们通过为所有$ q \ geq 9 $提供了此属性的$ q $颜色，在此问题上取得了第一个非平地进度，其中$ n $在$ n^{2+cq} $中指数为指数，而$ c> 0 $是绝对常数。
Erdős and Hajnal constructed a 4-coloring of the triples of an $N$-element set such that every $n$-element subset contains 2 triples with distinct colors, and $N$ is double exponential in $n$. Conlon, Fox and Rödl asked whether there is some integer $q\ge 3$ and a $q$-coloring of the triples of an $N$-element set such that every $n$-element subset has 3 triples with distinct colors, and $N$ is double exponential in $n$. We make the first nontrivial progress on this problem by providing a $q$-coloring with this property for all $q\geq 9$, where $N$ is exponential in $n^{2+cq}$ and $c>0$ is an absolute constant.
