Intrinsically Linked Graphs with Knotted Components

2007/05/15 by Thomas Fleming, Fleming, Thomas · 1 citation
Mathematics · #05C10 #57M15 #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:05C10 #msc:57M15 #msc:57M25

paper · pdf · doi:10.48550/arxiv.0705.2026

8 pages, 5 figures

arxiv created 2007/05/15 · arxiv updated 2009/12/01

Abstract

We construct a graph G such that any embedding of G into R³ contains a nonsplit link of two components, where at least one of the components is a nontrivial knot. Further, for any m < n we produce a graph H so that every embedding of H contains a nonsplit n component link, where at least m of the components are nontrivial knots. We then turn our attention to complete graphs and show that for any given n, every embedding of a large enough complete graph contains a two component link whose linking number is a nonzero multiple of n.

Cited by

• Some Ramsey-type results on intrinsic linking of n-complexes

Related

• Intrinsic linking and knotting are arbitrarily complex in directed graphs
• On intrinsically knotted and linked graphs
• Intrinsic knotting and linking of almost complete partite graphs
• Intrinsically Knotted and 4-Linked Directed Graphs
• Intrinsic knotting and linking of almost complete graphs