论文标题
树木的彩虹图
Rainbow Turán Methods for Trees
论文作者
论文摘要
RainbowTurán编号是研究经过良好的传统Turán数字的自然扩展，于2007年由Keevash，Mubayi，Sudakov和Verstraëte推出。图$ h $，$ ex^{*}（n，h）$的彩虹图师数量是$ n $顶点图$ g $的最大边缘，可以适当地颜色，没有彩虹$ h $ subgraph。 我们探讨了在彩虹图恩数字上找到上限的减少方法，并使用此方法为彩虹图恩（RainbowTurán）数量的双星，毛毛虫和完美的二进制树的结果提供信息。此外，我们定义了$ k $ - 唯一的着色和相关的$ k $turán号码。我们为经典问题的新变体提供了初步结果。
The rainbow Turán number, a natural extension of the well studied traditional Turán number, was introduced in 2007 by Keevash, Mubayi, Sudakov and Verstraëte. The rainbow Turán number of a graph $H$, $ex^{*}(n,H)$, is the largest number of edges for an $n$ vertex graph $G$ which can be properly edge colored with no rainbow $H$ subgraph. We explore the reduction method for finding upper bounds on rainbow Turán numbers, and use this to inform results for the rainbow Turán numbers of double stars, caterpillars, and perfect binary trees. In addition, we define $k$-unique colorings and the related $k$-unique Turán numbers. We provide preliminary results on this new variant on the classic problem.
