Year: 2026
Type: preprint
Abstract: 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 relying on computers; 2) An updated listing of obstructions in $\nabla\mathrm{Y}$ families including two new large families; 3) Connections with the Colin de Verdière's invariant including a new obstruction with $μ= 6$; and 4) Connectivity of obstructions and their structure near vertices of degree three or four. We address questions raised in earlier work, (re)state several conjectures, and propose new questions.
Source: arXiv (Cornell University)
Authors: Mattman, Thomas W, Pavelescu, Andrei
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167224464
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