Papers › Toroidal Embeddings of non-Intrinsically-Linked Graphs

Toroidal Embeddings of non-Intrinsically-Linked Graphs

18 Nov 2024arXiv:2411.12041links table onlyarchive 2025-07-28

Nathan Hall

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If a graph G can be embedded on the torus, and be embedded linklessly in ℝ³, 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 ℝ³, can be embedded linklessly in the standard torus.

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