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1)  connected spanning subgraph
2-连通支撑子图
2)  spanning subgraph
支撑子图
3)  2-connected graph
2-连通图
1.
Let G=(V;E) be a 2-connected graph of order n and k a positive integer, we consider the problem of partitioning G into k vertexdisjoint paths under the neighborhood union condition and them obtain the new following results: If ｜N_G(x_1)∪N_G(x_2)｜+｜N_G(y_1)∪N_G(y_2)｜n-k for every four independent vertices, then G can be partitioned into k vertex-disjoint paths.
给定一个阶为n的2-连通图G=(V;E)及一个正整数k,考虑在邻域并条件下G被分成k条点不交路的问题,得到下面的结果,对G中任何四个独立点x1,x2,y1,y2∈V,满足|NG(x1)∪NG(x2)|+|NG(y1)∪NG(y2)|n-k,则G能被分划分k条点不交的路。
2.
Any 2-connected graph on n vertices such that the degree sum of any two vertices at distance 2 is at least λ—1 contains a cycle of length at least λ.
若G是2-连通图,如对G中任何两个距离为2的点υ,ν都有d(υ)+d(ν)≥λ-1(5≤λ≤|V(G)|),则除了两类图外,G的最长圈的长至少为λ。
4)  2-connected graphs
2连通图
5)  connected subgraph
连通子图
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6)  2_edge_connected graph
2-边连通图
补充资料：的子
1.正妻所生的儿子。多指嫡长子。的﹐通"嫡"。
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