Geodesic
Intrinsically linked graphs and even linking number
Fleming, Thomas1 ; Diesl, Alexander2
1University of California San Diego, Department of Mathematics, 9500 Gilman Drive, La Jolla CA 92093-0112, USA
2University of California Berkeley, Department of Mathematics, 970 Evans Hall, Berkeley CA 94720-3840, USA
Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1419-1432
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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,k≠0, 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,k≠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.

DOI : 10.2140/agt.2005.5.1419
Keywords: intrinsically linked graph, spatial graph, graph embedding, linking number

Fleming, Thomas  1   ; Diesl, Alexander  2

1 University of California San Diego, Department of Mathematics, 9500 Gilman Drive, La Jolla CA 92093-0112, USA
2 University of California Berkeley, Department of Mathematics, 970 Evans Hall, Berkeley CA 94720-3840, USA 
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Fleming, Thomas; Diesl, Alexander. Intrinsically linked graphs and even linking number. Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1419-1432. doi: 10.2140/agt.2005.5.1419

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