Intrinsically linked graphs and even linking number

We study intrinsically linked graphs where we require that every embedding of the graph contains not just a non-split link, but a link that satisfies some additional property. Examples of properties we address in this paper are: a two component link with $l k (A, L) = k 2^{r}, k \neq 0$ , a non-split $n$ -component link where all linking numbers are even, or an $n$ -component link with components $L, A_{i}$ where $l k (L, A_{i}) = 3 k, k \neq 0$ . Links with other properties are considered as well.

For a given property, we prove that every embedding of a certain complete graph contains a link with that property. The size of the complete graph is determined by the property in question.

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Keywords

intrinsically linked graph, spatial graph, graph embedding, linking number

Mathematical Subject Classification 2000

Primary: 57M15

Secondary: 57M25, 05C10

References

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Publication

Received: 22 April 2004

Revised: 13 September 2005

Accepted: 20 September 2005

Published: 15 October 2005

Authors

Thomas Fleming
University of California San Diego Department of Mathematics 9500 Gilman Drive La Jolla CA 92093-0112 USA

Alexander Diesl
University of California Berkeley Department of Mathematics 970 Evans Hall Berkeley CA 94720-3840 USA

Volume 5, issue 4 (2005)

Thomas Fleming and Alexander Diesl

Abstract