**UM Math Graduate Students Seminar**

Dr. Anton Dochtermann

*University of Miami*

**will present**

**Links in embedded graphs **

Friday, October 19, 2012, 3:45pm

Ungar Building Room 402

**Abstract:**We say that a graph G is "intrinsically linked" if no matter how G is realized in 3-space, we can find a pair of disjoint cycles that are linked. About 30 years ago Conway and Gordon (and independently Sachs) showed that K_6, the complete graph on six vertices, is intrinsically linked. Analogous to planarity of graphs, the property of "having a linkless embedding" is minor-closed and hence admits a finite family of "forbidden minors". In 1995 Robertson, Seymour, and Thomas proved a conjecture of Sachs giving a characterization of this family (there are 7 such graphs, including the Petersen graph). We will discuss Conway and Gordon's proof and survey some related results. Although I might mention some fancy techniques, most of the talk will be from first principles. And yes there is a similar (albeit less complete) story for "intrinsically knotted" graphs.

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