论文标题
在平面的多重色数上
On upper bounds for the multi-fold chromatic numbers of the plane
论文作者
论文摘要
平面$χ_m$的多倍色数是最小的颜色$ k $，足以以恰好$ m $颜色的欧几里得飞机的每个点为每个点上色，因此，对于任何一对单位距离，彼此之间的任何一对点，两个相应的$ M $ -M $ -Subsets $ k $的$ k $ - set不包含任何常见的颜色。我们认为飞机的$ m $倍色数的上限。我们的主要结果是，对于任何$ m $，不平等$χ_m<（1+2/\ sqrt3）^2 \ cdot m+3.501 $保留。
The multi-fold chromatic number of the plane $χ_m$ is the smallest number of colors $k$, sufficient to color each point of the Euclidean plane in exactly $m$ colors, so that for any pair of points at a unit distance from each other, two corresponding $m$-subsets of $k$-set do not contain any common color. We consider upper bounds for $m$-fold chromatic numbers of the plane. Our main result is that for any $m$ the inequality $χ_m<(1+2/\sqrt3)^2\cdot m+3.501$ holds.
