论文标题
在毁灭图中的三角形上
On triangles in derangement graphs
论文作者
论文摘要
给定排列组$ g $，$ g $ $ g $ of $ g $的漏洞图是带有连接设置$ g $的所有扰动集的Cayley图。我们证明，当$ g $具有至少$ 3 $ $ 3 $时，$γ_g$包含一个三角形。 这项工作的动机是一个问题，即$γ_g$的独立数与$ g $中的稳定器的大小的比率。我们给出了该比率最大的及时群体的示例。
Given a permutation group $G$, the derangement graph $Γ_G$ of $G$ is the Cayley graph with connection set the set of all derangements of $G$. We prove that, when $G$ is transitive of degree at least $3$, $Γ_G$ contains a triangle. The motivation for this work is the question of how large can be the ratio of the independence number of $Γ_G$ to the size of the stabilizer of a point in $G$. We give examples of transitive groups where this ratio is maximum.
