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arXiv · 1210.1539

A generalization of Vassiliev's planarity criterion

Tyler Friesen
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Abstract

Motivated by his studies in knot theory V. Vassiliev introduced $X$-graphs as regular 4-valent graph with a structure of pairs of opposite edges at each vertex. He conjectured the conditions under which $X$-graph can be embedded into a plane respecting the the $X$-structure at every vertex. The conjecture was proved by V.Manturov. Here we generalize these results for graphs with vertices of valency 4 or 6, *-graphs. A problem of such generalization was posted by A.Skopenkov.

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Tyler Friesen. 2012-10-04. A generalization of Vassiliev's planarity criterion. https://arxiv.org/abs/1210.1539

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