半传递重图的限制性边连通度（英文）

On Restricted Edge-connectivity of Half-transitive Multigraphs

设G=(V,E)是一个重图(包含重边,但不含环).图G的边连通度,记为λ(G),是G的最小边割的基数.我们称G是极大边连通的如果λ(G)=δ(G);称图G是超边连通的如果每个最小边割都是某个点的邻边集合.图G的限制性边连通度,记为λ(G),是图G的最小限制性边割的基数.如果λ(G)达到限制性边连通度的上界,我们称G是λ-最优的.一个二部重图是半传递的如果它作用在每个部分上都是传递的.在本文中,我们将刻画极大边连通的、超边连通的、λ-最优的半传递重图.

Let G =（V, E） be a multigraph（it has multiple edges, but no loops）. The edge connectivity, denoted byλ（G）, is the cardinality of a minimum edge-cut of G. We call G maximally edge-connected if λ（G） = δ（G）, and G super edge-connected if every minimum edge-cut is a set of edges incident with some vertex. The restricted edge-connectivityλ（G） of G is the minimum number of edges whose removal disconnects G into non-trivial components. If λ（G） achieves the upper bound of restricted edge-connectivity, then G is said to be λ-optimal. A bipartite multigraph is said to be half-transitive if its automorphism group is transitive on the sets of its bipartition. In this paper, we will characterize maximally edge-connected half-transitive multigraphs, super edge-connected half-transitive multigraphs, and λ-optimal half-transitive multigraphs.