A graph is called intrinsically knotted if every embedding of in contains a nontrivial knot.
Example: , the complete graph on 7 vertices, was proven to be intrinsically knotted by Conway and Gordon.
The property of being not intrinsically knotted is inherited by minors. That is, if a graph is not intrinsically knotted and the graph can be obtained from by deleting or contracting edges, then is also not intrinsically knotted.
According to the Robertson-Seymour Theorem (also known as Wagner’s Conjecture), this means that the obstruction set for this property must be finite. Thus there are only a finite number of intrinsically knotted graphs which are minor minimal, that is, for which any graph obtained by edge deletion or contraction is not intrinsically knotted. As of the creation of this article (06/01/2008), this set is still not known.
|Date of creation||2013-03-22 18:06:08|
|Last modified on||2013-03-22 18:06:08|
|Last modified by||YourInnerNurmo (20577)|