A graph is intrinsically linked if any embedding of in contains a nontrivial link.
Example: , the complete graph on 6 vertices, was proven to be intrinsically linked by Conway and Gordon.
The property of being not intrinsically linked is inherited by minors. That is, if is not intrinsically linked and can be obtained from by edge contractions or deletions, then is also not intrinsically linked.
By the Robertson-Seymour Theorem (formerly Wagner’s Conjecture), the obstruction set for this property must be finite. This means that the set of minor minimal intrinsically linked graphs is finite. In fact, there are 7 graphs in this set; it is known as the Petersen family, and it consists of graphs which can be obtained from by repeated -Y or Y- transformations.
|Date of creation||2013-03-22 18:06:11|
|Last modified on||2013-03-22 18:06:11|
|Last modified by||YourInnerNurmo (20577)|