## Knot a Graph? Why Not? |

**Susan Beckhardt**

SUNY @ Albany

October 13, 2008

4:30 pm

Bailey Hall 207

Refreshments will be served at 4:15 in Bailey Hall 204

Pick seven points in space and connect each pair of points with a curve, and what you get is a spatial embedding of K_{7 }, the complete graph on seven vertices. No matter how you arrange the vertices and edges, I can always find a closd path that is tied in a knot. A graph with this property, that every spatial embedding has a knotted cycle, is said to be intrinsically knotted.In 1983 John Conway and Cameron Gordon proved that K

_{7}is intrinsically knotted. We'll discuss their proof, which requires no background other than some basic combinatorics, and explore some of the intriguing results and questions that have arisen since then.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Sun Apr 22 04:28:39 EDT 2018 |