English

A generalization of Vassiliev's planarity criterion

Combinatorics 2012-10-05 v1 Geometric Topology

Abstract

Motivated by his studies in knot theory V. Vassiliev introduced XX-graphs as regular 4-valent graph with a structure of pairs of opposite edges at each vertex. He conjectured the conditions under which XX-graph can be embedded into a plane respecting the the XX-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.

Keywords

Cite

@article{arxiv.1210.1539,
  title  = {A generalization of Vassiliev's planarity criterion},
  author = {Tyler Friesen},
  journal= {arXiv preprint arXiv:1210.1539},
  year   = {2012}
}