Intrinsic Knotting and Linking of Complete Graphs

Authors

Erica Flapan, Pomona CollegeFollow

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2002

Keywords

Embedded graphs, intrinsic knotting, intrinsic linking

Abstract

We show that for every m∈N, there exists an n∈N such that every embedding of the complete graph K_n in R³ contains a link of two components whose linking number is at least m. Furthermore, there exists an r∈N such that every embedding of K_r in R³ contains a knot Q with |a₂(Q)| ≥ m, where a₂(Q) denotes the second coefficient of the Conway polynomial of Q.

Comments

Posted with the permission of Mathematical Sciences Publishers.

Rights Information

© 2002 Mathematical Sciences Publishers

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.2140/agt.2002.2.371

Recommended Citation

E. Flapan, Intrinsic Knotting and Linking of Complete Graphs, Algebraic and Geometric Topology, Vol 2, (2002) 371-380. doi: 10.2140/agt.2002.2.371