局部连通图的群Z3-连通性
GROUP Z3-CONNECTIVITY IN LOCALLY CONNECTED GRAPH

本文研究了局部连通图的群连通性的问题.利用不断收缩非平凡Z3-连通子图的方法,在G是3-边连通且局部连通的无爪无沙漏图的情况下,获得了G不是群Z3-连通的当且仅当G是K4或W5.推广了当G是2-边连通且局部3-边连通时,G是群Z3-连通的这个结果.
On this paper, we investigate group connectivity of locally connected groups. Suppose that G is a 3-edge-connected and locally connected simple graph with {H,K1,3}-free. By repeatedly contracting nontrivial Z3-connected subgraph of G, we obtain that G is not Z3-connected if and only if G is K4 or W5, which generalizes the result that G is Z3-connected if G is 2-edge-connected and locally 3-edge-connected