摘要
Let G be a 2-edge-connected simple graph on n vertices. For an edge e = uv ∈ E（G）, define d（e） = d（u） ＋ d（v）. Let F denote the set of all simple 2-edge-connected graphs on n ） 4 vertices such that G∈ F if and only if d（e） ＋ d（e′） ≥ 2n for every pair of independent edges e, e′ of G. We prove in this paper that for each G ∈ F, G is not Z3-connected if and only if G is one of K2,n-2, K3,n-3, K^＋2,n-2,K^＋ 3,n-3 or one of the 16 specified graphs, which generalizes the results of X. Zhang et al. [Discrete Math., 20]0, 310： 3390-3397] and G. Fan and X. Zhou [Discrete Math., 2008, 308： 6233-6240].
Let G be a 2-edge-connected simple graph on n vertices. For an edge e = uv ∈ E（G）, define d（e） = d（u） ＋ d（v）. Let F denote the set of all simple 2-edge-connected graphs on n ） 4 vertices such that G∈ F if and only if d（e） ＋ d（e′） ≥ 2n for every pair of independent edges e, e′ of G. We prove in this paper that for each G ∈ F, G is not Z3-connected if and only if G is one of K2,n-2, K3,n-3, K^＋2,n-2,K^＋ 3,n-3 or one of the 16 specified graphs, which generalizes the results of X. Zhang et al. [Discrete Math., 20]0, 310： 3390-3397] and G. Fan and X. Zhou [Discrete Math., 2008, 308： 6233-6240].
基金
Acknowledgements The first author was supported by the Excellent Doctorial Dissertation Cultivation Grant from Huazhong Normal University （2013YBYB42）. The second author was supported in part by the National Natural Science Foundation of China （Grant No. 11171129） and the Doctoral Fund of Ministry of Education of China （Grant No. 20130144110001）.
