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 , a non-split -component link where all linking numbers are even, or an -component link with components where . 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 graphs and even linking number." Algebr. Geom. Topol. 5 (4) 1419 - 1432, 2005. https://doi.org/10.2140/agt.2005.5.1419