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Intrinsically linked graphs and even linking number

Thomas Fleming·Alexander Diesl
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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.

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Thomas Fleming, Alexander Diesl. 2005-11-05. Intrinsically linked graphs and even linking number. https://doi.org/10.2140/agt.2005.5.1419

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