Toroidal Embeddings of non-Intrinsically-Linked Graphs

Nathan Hall

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arXiv · 2411.12041

Toroidal Embeddings of non-Intrinsically-Linked Graphs

Nathan Hall

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Abstract

If a graph $G$ can be embedded on the torus, and be embedded linklessly in $\mathbb{R}^3$, it's not known whether or not we can always find a linkless embedding of $G$ contained in the standard (unknotted) torus; We show that, for orders 9 and below, any graph which is both embeddable on the torus, and linklessly in $\mathbb{R}^3$, can be embedded linklessly in the standard torus.

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Nathan Hall. 2024-11-18. Toroidal Embeddings of non-Intrinsically-Linked Graphs. https://arxiv.org/abs/2411.12041

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