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Intrinsically linked graphs and even linking number

Thomas Fleming and Alexander Diesl

Algebraic & Geometric Topology 5 (2005) 1419–1432

arXiv: math.GT/0511133


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) = k2r,k0, a non-split n-component link where all linking numbers are even, or an n-component link with components L,Ai where lk(L,Ai) = 3k,k0. 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.

intrinsically linked graph, spatial graph, graph embedding, linking number
Mathematical Subject Classification 2000
Primary: 57M15
Secondary: 57M25, 05C10
Forward citations
Received: 22 April 2004
Revised: 13 September 2005
Accepted: 20 September 2005
Published: 15 October 2005
Thomas Fleming
University of California San Diego
Department of Mathematics
9500 Gilman Drive
La Jolla CA 92093-0112
Alexander Diesl
University of California Berkeley
Department of Mathematics
970 Evans Hall
Berkeley CA 94720-3840