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Degree sum of a pair of independent edges and Z 3-connectivity

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Abstract

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 Z 3-connected if and only if G is one of K 2,n−2, K 3,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., 2010, 310: 3390–3397] and G. Fan and X. Zhou [Discrete Math., 2008, 308: 6233–6240].

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Authors and Affiliations

  1. Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China

    Ziwen Huang & Xiangwen Li

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  1. Ziwen Huang
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  2. Xiangwen Li
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Correspondence to Xiangwen Li.

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Huang, Z., Li, X. Degree sum of a pair of independent edges and Z 3-connectivity. Front. Math. China 11, 1533–1567 (2016). https://doi.org/10.1007/s11464-015-0457-z

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  • DOI: https://doi.org/10.1007/s11464-015-0457-z

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