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arXiv · 2407.09476

Intrinsically knotted graphs and connected domination

Gregory Li·Andrei Pavelescu·Elena Pavelescu
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Abstract

We classify all the maximal linklessly embeddable graphs of order 12 and show that their complements are all intrinsically knotted. We derive results about the connected domination numbers of a graph and its complement. We provide an answer to an open question about the minimal order of a 3-non-compliant graph. We prove that the complements of knotlessly embeddable graphs of order at least 15 are all intrinsically knotted. We provide results on general $k$-non-compliant graphs and leave a set of open questions for further exploration of the subject.

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Gregory Li, Andrei Pavelescu, Elena Pavelescu. 2024-07-12. Intrinsically knotted graphs and connected domination. https://arxiv.org/abs/2407.09476

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