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Topological Graph Theory

Graphs Session #5 #2

Subevent of Graphs Session #5

Central Time (US & Canada)

Starts at: 2025-08-14 09:00AM

Ends at: 2025-08-14 09:25AM

Obstructions to knotless embedding

Hyoungjun Kim ⟨kimhjun@knu.ac.kr⟩

Abstract:

The Graph Minor Theorem of Robertson and Seymour implies a finite set of obstructions for any minor closed graph property. We show that there are only three obstructions to knotless embedding of size 23, which is far fewer than the 92 of size 22 and the hundreds known to exist at larger sizes. We describe several other topological properties whose obstruction set demonstrates a similar dip at small size. For order ten graphs, we classify the 35 obstructions to knotless embedding and the 49 maximal knotless graphs. This work is collaborated with Thomas Mattman.

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