Given a permutation group G, the derangement graph ${\mathrm{\Gamma }}_G$ 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, ${\mathrm{\Gamma }}_G$ contains a triangle.

The motivation for this work is the question of how large can be the ratio of the independence number of ${\mathrm{\Gamma }}_G$ to the size of the stabilizer of a point in G. We give examples of transitive groups where this ratio is maximum.

中文翻译：

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在排列图中的三角形上

给定排列组G，排列图${\mathrm{\Gamma }}_G$的ģ是该组的所有紊乱的Cayley图与连接组G ^。我们证明，当G传递的度数至少为3时，${\mathrm{\Gamma }}_G$ 包含一个三角形。

进行这项工作的动机是一个问题，即： ${\mathrm{\Gamma }}_G$到G点的稳定器的大小。我们举例说明该比例最大的传递组。