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摘要: 证明了如下结果:(1) 一个2-连通图的⊙-图是2(p-1)连通的; (2)如果一个2-连通图G有两个单圈支撑子图, 且这两个单圈支撑子图分别含m和n个悬挂点(mn), 则图G至少有2(p-1)个含k个悬挂点的单圈支撑子图, 这里m≦k≦n, p=|E(G)|-|V(G)|+1.Abstract: This paper proved the following results:(1) The ⊙-graph of a 2-connected graph is 2(p-1) connected; (2) if a 2-connected graph G has two unicyclic spanning subgraphs and the number of one-valent vertices of these two subgraphs are respectively m and n (mn), then for any integer k:m≦k≦n,there exist at least 2(p-1) unicyclic subgraphs of graph G whick have k one-valent vertices. Here, p is the dimension of the cycle space of G.
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