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/