论文标题
空的彩虹三角形$ k $彩色点套装
Empty Rainbow Triangles in $k$-colored Point Sets
论文作者
论文摘要
让$ s $是一组$ n $点在飞机上的总位置。假设$ s $的每个点都被分配了$ k \ ge 3 $可能的颜色之一，并且每个颜色类别的点相同数字，$ m $。 $ s $上的带顶点的多边形如果不包含内部$ s $的点，则是空的；如果其所有顶点都有不同的颜色，那就是彩虹。令$ f（k，m）$为由$ s $确定的空彩虹三角形的最小数量。在本文中，我们为此功能提供了紧密的渐近范围。此外，我们表明$ s $可能无法决定一些任意较大的$ k $和$ m $的空彩虹四边形。
Let $S$ be a set of $n$ points in general position in the plane. Suppose that each point of $S$ has been assigned one of $k \ge 3$ possible colors and that there is the same number, $m$, of points of each color class. A polygon with vertices on $S$ is empty if it does not contain points of $S$ in its interior; and it is rainbow if all its vertices have different colors. Let $f(k,m)$ be the minimum number of empty rainbow triangles determined by $S$. In this paper we give tight asymptotic bounds for this function. Furthermore, we show that $S$ may not determine an empty rainbow quadrilateral for some arbitrarily large values of $k$ and $m$.
