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A note on Z 3-connected graphs with degree sum condition

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Abstract

A graph G satisfies the Ore-condition if d(x)+d(y) ≥ |V(G)| for any xy ∉ E(G). Luo et al. [European J. Combin., 2008 characterized the simple Z 3-connected graphs satisfying the Ore-condition. In this paper, we characterize the simple Z 3-connected graphs G satisfying d(x) + d(y) ≥ |V(G)| − 1 for any xy ∈ E(G), which improves the results of Luo et al.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, P. R. China

    Xin Min Hou

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  1. Xin Min Hou
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Correspondence to Xin Min Hou.

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Supported by National Natural Science Foundation of China (Grant No. 11071233) and the Fundamental Research Funds for the Central Universities (Grant No. WK0010000021)

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Hou, X.M. A note on Z 3-connected graphs with degree sum condition. Acta. Math. Sin.-English Ser. 28, 2161–2168 (2012). https://doi.org/10.1007/s10114-012-0710-2

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  • DOI: https://doi.org/10.1007/s10114-012-0710-2

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