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Graphs that contain multiply transitive matchings
European Journal of Combinatorics ( IF 1 ) Pub Date : 2020-09-07 , DOI: 10.1016/j.ejc.2020.103236
Alex Schaefer , Eric Swartz

Let Γ be a finite, undirected, connected, simple graph. We say that a matching M is a permutable m-matching if M contains m edges and the subgroup of Aut(Γ) that fixes the matching M setwise allows the edges of M to be permuted in any fashion. A matching M is 2-transitive if the setwise stabilizer of M in Aut(Γ) can map any ordered pair of distinct edges of M to any other ordered pair of distinct edges of M. We provide constructions of graphs with a permutable matching; we show that, if Γ is an arc-transitive graph that contains a permutable m-matching for m4, then the degree of Γ is at least m; and, when m is sufficiently large, we characterize the locally primitive, arc-transitive graphs of degree m that contain a permutable m-matching. Finally, we classify the graphs that have a 2-transitive perfect matching and also classify graphs that have a permutable perfect matching.



中文翻译:

包含多重传递匹配的图

Γ是一个有限的,无向的,连通的,简单的图。我们说一个匹配中号可置换的 -如果匹配中号 包含 边和的子组 utΓ 修复匹配 中号 setwise允许的边缘 中号以任何方式排列。配套中号如果...的设定稳定器为2-可传递中号utΓ 可以映射任何有序对的不同边缘 中号 到任何其他有序对的不同边 中号。我们提供具有可置换匹配的图的构造;我们证明,如果Γ 是包含可置换的弧形传递图 -匹配 4,则度 Γ 至少是 ; 什么时候 足够大,我们表征度的局部原始的,弧形传递图 包含置换 -匹配。最后,我们对具有2个传递完全匹配的图进行分类,并对具有可置换完美匹配的图进行分类。

更新日期:2020-09-07
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