On Virtual Crossing Numbers for Virtual Knots
Geometric Topology
2011-07-26 v1
Abstract
The aim of the present paper is to prove that the minimal number of virtual crossings for some families of virtual knots grows quadratically with respect to the minimal number of classical crossings. All previously known estimates for virtual crossing number were principally no more than linear in the number of classical crossings (or, what is the same, in the number of edges of a virtual knot diagram) and no virtual knot was found with virtual crossing number greater than the classical crossing number.
Keywords
Cite
@article{arxiv.1107.4828,
title = {On Virtual Crossing Numbers for Virtual Knots},
author = {Vassily Olegovich Manturov},
journal= {arXiv preprint arXiv:1107.4828},
year = {2011}
}