Kenji Kozai

Harvey Mudd College Mathematics 2008

Thesis Proposal: Intrinsic Properties of Graphs
Submitted Thesis Intrinsic Linking and Knotting of Graphs
Thesis Advisor: Prof. David Backman
Second Reader: Prof. Francis Edward Su

Intrinsic Linking and Knotting of Graphs

An analog to intrinsic linking, intrinsic even linking, is explored. Four graphs are established to be minor minimal intrinsically even linked, and it is conjectured that they form a complete minor minimal set. One goal is to prove the completeness of the minor minimal set.

The other component investigates a new approach to intrinsic knotting. By adapting knot energy to graphs, it is hoped that intrinsic knotting can be detected through direct computation.