Affiliation:
1. Department of Mathematics, University of California San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0112, USA
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 2-component link whose linking number is a nonzero multiple of n. Finally, we show that if a graph is a Cartesian product of the form G × K2, it is intrinsically linked if and only if G contains one of K5, K3,3 or K4,2 as a minor.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
4 articles.
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