3 papers
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…
math.CO2024
Intrinsically knotted graphs and connected domination
Gregory Li, Andrei Pavelescu, Elena Pavelescu
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…