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There are too many knotted graphs!Geometry/Topology
|Speaker:||Thomas Mattman, CSU Chico|
|Start time:||Tue, Apr 26 2016, 1:10PM|
(Joint with Goldberg and Naimi)
The powerful Graph Minor Theorem of Robertson and Seymour ensures that, for any graph property, whatsoever, there is an associated finite list of graphs that are minor minimal with respect to that property. For example, with Thomas, they show that the seven graphs in the Petersen family are exactly the minor minimal intrinsic linked (MMIL) graphs.
A graph is intrinsically linked (knotted) if every embedding in $\R^3$ has
a pair of non-trivially linked cycles (a non-trivially knotted cycle).
Through 2003, 41 MMIK (minor minimal intrinsically knotted) graphs were
known. We have 220 new examples and our methods suggest there are likely
``many, many more.''