TL;DR
This paper presents a novel proof of Vassiliev's planarity criterion for framed four-valent graphs, utilizing the Pontryagin-Kuratowski theorem to establish the result.
Contribution
It introduces a new proof method for Vassiliev's conjecture, connecting planarity criteria with classical topological theorems.
Findings
New proof of Vassiliev's planarity criterion
Connection between planarity and Pontryagin-Kuratowski theorem
Extension to *-graphs
Abstract
We give a new proof of Vassiliev's planarity criterion for framed four-valent graphs (and more generally, *-graphs), which is based on Pontryagin-Kuratowski theorem.
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