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The 3-Connected Graphs with Exactly k Non-Essential Edges

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Abstract

Let G be a simple 3-connected graph. An edge e of G is essential if neither the deletion G\ e nor the contraction G/e is both simple and 3-connected. In this study, we show that all 3-connected graphs with k(k ≥ 2) non-essential edges can be obtained from a wheel by three kinds of operations which defined in the paper.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Gannan Normal University, 341000, Jiangxi, China

    Yuxing Liu

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  1. Yuxing Liu
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Correspondence to Yuxing Liu.

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Liu, Y. The 3-Connected Graphs with Exactly k Non-Essential Edges. Graphs and Combinatorics 26, 119–131 (2010). https://doi.org/10.1007/s00373-010-0873-5

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  • DOI: https://doi.org/10.1007/s00373-010-0873-5

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