Algebraic and Geometric Topology 5 (2005), paper no. 55, pages 1419-1432.

Intrinsically linked graphs and even linking number

Thomas Fleming, Alexander Diesl

Abstract. 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 lk(A,L) = k2^r, k not 0, a non-split n-component link where all linking numbers are even, or an n-component link with components L, A_i where lk(L,A_i) = 3k, k not 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.

Keywords. Intrinsically linked graph, spatial graph, graph embedding, linking number

AMS subject classification. Primary: 57M15. Secondary: 57M25,05C10.

E-print: arXiv:math.GT/0511133

DOI: 10.2140/agt.2005.5.1419

Submitted: 22 April 2004. (Revised: 13 September 2005.) Accepted: 20 September 2005. Published: 15 October 2005.

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Thomas Fleming, Alexander Diesl
University of California San Diego, Department of Mathematics
9500 Gilman Drive, La Jolla, CA 92093-0112, USA
and
University of California Berkeley, Department of Mathematics
970 Evans Hall, Berkeley, CA 94720-3840, USA
Email: tfleming@math.ucsd.edu, adiesl@math.berkeley.edu

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