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An Infinite Family of Linklessly Embeddable Tutte-4-Connected Graphs

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Abstract

For each \(n\ge 14\), we provide an example of a linklessly embeddable, Tutte-4-connected graph of order n. We start with a linklessly embeddable, Tutte-4-connected graph of order fourteen, and we perform 4-vertex splittings to inductively build the family of triangle free, 4-connected graphs. We prove the graphs we constructed are linklessly embeddable, as minors of clique sums over \(K_4\) of linklessly embeddable graphs.

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  1. University of South Alabama, Mobile, AL, 36688, USA

    Andrei Pavelescu & Elena Pavelescu

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  1. Andrei Pavelescu
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  2. Elena Pavelescu
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Correspondence to Elena Pavelescu.

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Pavelescu, A., Pavelescu, E. An Infinite Family of Linklessly Embeddable Tutte-4-Connected Graphs. Graphs and Combinatorics 38, 96 (2022). https://doi.org/10.1007/s00373-022-02497-9

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  • DOI: https://doi.org/10.1007/s00373-022-02497-9

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