论文标题
彩虹饱和
Rainbow Saturation
论文作者
论文摘要
我们引入了彩虹饱和度和相应的彩虹饱和数字的概念。这是彩虹图恩数字的饱和版本，其系统的研究是由Keevash，Mubayi，Sudakov和Verstraëte发起的。我们提供了彩虹饱和数远离普通饱和数的图表的示例。这包括所有完整的图形$ k_n $，for $ n \ geq 4 $和几个二分图。值得注意的是，这种情况是这样的，因为在彩虹极端数字与传统的极端数字相比，这并没有发生。我们还表明，饱和数对于大量的图表是线性的，它提供了众所周知的Kásonyi和Tuza定理的部分彩虹类似物。我们以相关的开放式问题和猜想结束了本文。
We introduce a notion of rainbow saturation and the corresponding rainbow saturation number. This is the saturation version of the rainbow Turán numbers whose systematic study was initiated by Keevash, Mubayi, Sudakov, and Verstraëte. We give examples of graphs for which the rainbow saturation number is bounded away from the ordinary saturation number. This includes all complete graphs $K_n$ for $n\geq 4$, and several bipartite graphs. It is notable that there are non-bipartite graphs for which this is the case, as this does not happen when it comes to the rainbow extremal number versus the traditional extremal number. We also show that saturation numbers are linear for a large class of graphs, providing a partial rainbow analogue of a well known theorem of Kásonyi and Tuza. We conclude this paper with related open questions and conjectures.
