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math.GT2026
Three thousand obstructions to knotless embedding
Thomas W Mattman, Andrei Pavelescu
We present a list of 3028 obstructions to knotless embedding. We survey recent work in this area including: 1) A bibliography of graphs proven to be intrinsically knotted without r…
math.CO2026
New minor minimal non-apex graphs
Andrei Pavelescu, Elena Pavelescu, Madeline Potter
A graph is apex if it becomes planar after the deletion of one vertex. The family of apex graphs is closed under taking minors, so it is characterized by a finite set of forbidden…