论文标题
避免彩虹子图的极端结果
Extremal results for graphs avoiding a rainbow subgraph
论文作者
论文摘要
我们说$ k $ graphs $ g_1，g_2，\ dots，dots，g_k $ y of size $ n $的尺寸$ n $包含一个图形$ h $的彩虹副本，如果它们的联盟包含$ h $的副本，每个边缘都属于独特的$ g_i $。我们为弗兰克尔（Frankl）的猜想提供了一个反例，以三个图的边缘组的最大乘积避免了彩虹三角形。我们提出了一个替代猜想，我们在这三个图的结合完成的其他假设下证明了这一点。此外，我们确定了三个图或四个图的边缘集的最大乘积，避免了三个长度的彩虹路径。
We say that $k$ graphs $G_1,G_2,\dots,G_k$ on a common vertex set of size $n$ contain a rainbow copy of a graph $H$ if their union contains a copy of $H$ with each edge belonging to a distinct $G_i$. We provide a counterexample to a conjecture of Frankl on the maximum product of the sizes of the edge sets of three graphs avoiding a rainbow triangle. We propose an alternative conjecture, which we prove under the additional assumption that the union of the three graphs is complete. Furthermore, we determine the maximum product of the sizes of the edge sets of three graphs or four graphs avoiding a rainbow path of length three.
