This paper has been withdrawn by Gelasio Salazar
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Abstract:A plane graph $H$ is a {\em plane minor} of a plane graph $G$ if there is a sequence of vertex and edge deletions, and edge contractions performed on the plane, that takes $G$ to $H$. Motivated by knot theory problems, it has been asked if the plane minor relation is a well-quasi-order. We settle this in the affirmative. We also prove an additional application to knot theory. If $L$ is a link and $D$ is a link diagram, write $D\leadsto L$ if there is a sequence of crossing exchanges and smoothings that takes $D$ to a diagram of $L$. We show that, for each fixed link $L$, there is a polynomial-time algorithm that takes as input a link diagram $D$ and answers whether or not $D\leadsto L$.
From: Gelasio Salazar [view email]
[v1]
Mon, 6 May 2019 06:01:58 UTC (85 KB)
[v2]
Sat, 1 Aug 2026 19:23:19 UTC (1 KB) (withdrawn)
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