Well-quasi-orders proved on embedded planar graphs.
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Study shows quasipositive fiber surfaces can't be well-ordered.
Proves a quasi-order on fibre surfaces of positive braid links.
A plane graph is a {\em plane minor} of a plane graph if there is a sequence of vertex and edge deletions, and edge contractions performed on the plane, that takes to . Motivated by knot theory problems, it has been asked if the plane minor relation is a well-quasi-order. We settle this in the affirmativ…
Authors show that genus defects of Hopf arborescent links are decidable.
The paper is partially withdrawn: in its current form, Lemma 2.3 is false, so that our proof of Theorem A and Proposition B has an important gap. We were unable to fix it yet. Any help is most welcome. We prove that the restriction of surface minority to fiber surfaces of divides is a well-quasi-order. Here surface min…