European Journal of Combinatorics ( IF 1 ) Pub Date : 2020-09-07 , DOI: 10.1016/j.ejc.2020.103236 Alex Schaefer , Eric Swartz
Let be a finite, undirected, connected, simple graph. We say that a matching is a permutable -matching if contains edges and the subgroup of that fixes the matching setwise allows the edges of to be permuted in any fashion. A matching is 2-transitive if the setwise stabilizer of in can map any ordered pair of distinct edges of to any other ordered pair of distinct edges of . We provide constructions of graphs with a permutable matching; we show that, if is an arc-transitive graph that contains a permutable -matching for , then the degree of is at least ; and, when is sufficiently large, we characterize the locally primitive, arc-transitive graphs of degree that contain a permutable -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
让 是一个有限的,无向的,连通的,简单的图。我们说一个匹配是可置换的 -如果匹配 包含 边和的子组 修复匹配 setwise允许的边缘 以任何方式排列。配套如果...的设定稳定器为2-可传递 在 可以映射任何有序对的不同边缘 到任何其他有序对的不同边 。我们提供具有可置换匹配的图的构造;我们证明,如果 是包含可置换的弧形传递图 -匹配 ,则度 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。