论文标题
在反拉姆西的阈值上
On the anti-Ramsey threshold for non-balanced graphs
论文作者
论文摘要
对于Graphs $ g $和$ h $，我们编写$ g \ overset {\ mathrm {rb}} {\ longrightArrow} h $，如果$ g $的任何适当的边缘颜色包含$ h $的彩虹副本，即，副本的颜色不超过一次。 Kohayakawa，Konstadinidis和最后一位作者证明，$ g（n，p）\ Overset {\ Mathrm {rb}} {\ longrightArrow} h $的门槛最多是$ n^{ - 1/m_2（h）} $。先前的结果与该抗斑点阈值的下限与至少5个顶点的完整图相匹配。 kohayakawa，konstadinidis和最后一位作者还提出了一个无限的图$ h $家族，抗拉姆西阈值渐近地小于$ n^{ - 1/m_2（h）} $。在本文中，我们设计了一个框架，该框架提供了一个更丰富，更复杂的此类图，其中包括所有先前已知的示例。
For graphs $G$ and $H$, we write $G \overset{\mathrm{rb}}{\longrightarrow} H $ if any proper edge-coloring of $G$ contains a rainbow copy of $H$, i.e., a copy where no color appears more than once. Kohayakawa, Konstadinidis and the last author proved that the threshold for $G(n,p) \overset{\mathrm{rb}}{\longrightarrow}H$ is at most $n^{-1/m_2(H)}$. Previous results have matched the lower bound for this anti-Ramsey threshold for cycles and complete graphs with at least 5 vertices. Kohayakawa, Konstadinidis and the last author also presented an infinite family of graphs $H$ for which the anti-Ramsey threshold is asymptotically smaller than $n^{-1/m_2(H)}$. In this paper, we devise a framework that provides a richer and more complex family of such graphs that includes all the previously known examples.
