论文标题
柔和的色彩颜色
Trivial colors in colorings of Kneser graphs
论文作者
论文摘要
我们表明，带有$ n-2k+2 $颜色的旋转图的任何适当着色$ kg_ {n，k} $包含一种微不足道的颜色（即，包含固定元素的颜色），提供$ n>（2+ \ varepsilon）k^2 $，其中$ \ varepsilon \ af $ as $ as $ as $ as $ as $ as $ affty $。这个界限本质上很紧。这是对正确颜色$ kg_ {n，k} $所需的最小数量的非平凡颜色数量的更一般结果的结果。
We show that any proper coloring of a Kneser graph $KG_{n,k}$ with $n-2k+2$ colors contains a trivial color (i.e., a color consisting of sets that all contain a fixed element), provided $n>(2+\varepsilon)k^2$, where $\varepsilon\to 0$ as $k\to \infty$. This bound is essentially tight. This is a consequence of a more general result on the minimum number of non-trivial colors needed to properly color $KG_{n,k}$.
