Knot a Graph? Why Not?
SUNY @ Albany
October 13, 2008
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 K7 , 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 K7 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.
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