This paper introduces a self-linking invariant for virtual knots and links, and relates this invariant to a state model called the binary bracket, and to a class of coloring problems for knots and links that include classical coloring problems for cubic graphs.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-10,
author = {Louis H. Kauffman},
title = {A self-linking invariant of virtual knots},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {135-158},
zbl = {1064.57004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-10}
}
Louis H. Kauffman. A self-linking invariant of virtual knots. Fundamenta Mathematicae, Tome 184 (2004) pp. 135-158. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-10/