Searching for missing links. The evolution of an undergraduate research project
May 16, 2002
Bailey Hall 106
In 1983, Horst Sachs, John Conway and Cameron Gordon proved that any spatial embedding of K6, the complete graph on six vertices, contains a pair of linked 3-cycles. A graph that contains a link in all of its embeddings is called an intrinsically linked graph. The class of intrinsically linked graphs was completely characterized in 1995 by N. Robertson, P. Seymour, and R. Thomas. For those graphs that are known to be intrinsically linked, we are interested in determining the size of the cycles in the links. We show that for any spatial embedding of Kn, the complete graph on n > 2 vertices, and any choice of s,t > 2 with s+t=n, there will be a link consisting of an s-cycle and a t-cycle. This is joint work with William Johnson '02 with help from David Bokor '00, Daniela Chiulli '99 and Julius Barbanel.
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