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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