Intrinsically linked graphs and even linking number
Thomas R. Fleming, Alexander J. Diesl · Algebraic & Geometric Topology · 2005
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 = 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 = 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.