论文标题
顶点传播超图的边缘连接性
The Edge-Connectivity of Vertex-Transitive Hypergraphs
论文作者
论文摘要
如果图形或超图具有顶点的自动形态群在其顶点上作用，则将其图形传递。 Mader的经典定理断言，每个连接的顶点传递图都是最大的边缘连接。我们将此结果概括为超图，并表明每个连接的线性均匀顶点传输超图都是最大的边缘连接。我们还表明，如果我们在此概括中放松线性或统一条件，那么我们可以构建顶点传播的超图的示例，这些示例不是最大的边缘连接。
A graph or hypergraph is said to be vertex-transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex-transitive graph is maximally edge-connected. We generalise this result to hypergraphs and show that every connected linear uniform vertex-transitive hypergraph is maximally edge-connected. We also show that if we relax either the linear or uniform conditions in this generalisation, then we can construct examples of vertex-transitive hypergraphs which are not maximally edge-connected.
