Involve: A Journal of Mathematics
- Volume 1, Number 2 (2008), 145-158.
On graphs for which every planar immersion lifts to a knotted spatial embedding
We call a graph intrinsically linkable if there is a way to assign over/under information to any planar immersion of such that the associated spatial embedding contains a pair of nonsplittably linked cycles. We define intrinsically knottable graphs analogously. We show there exist intrinsically linkable graphs that are not intrinsically linked. (Recall a graph is intrinsically linked if it contains a pair of nonsplittably linked cycles in every spatial embedding.) We also show there are intrinsically knottable graphs that are not intrinsically knotted. In addition, we demonstrate that the property of being intrinsically linkable (knottable) is not preserved by vertex expansion.
Involve, Volume 1, Number 2 (2008), 145-158.
Received: 10 June 2007
Accepted: 1 December 2007
First available in Project Euclid: 20 December 2017
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DeCelles, Amy; Foisy, Joel; Versace, Chad; Wilson, Alice. On graphs for which every planar immersion lifts to a knotted spatial embedding. Involve 1 (2008), no. 2, 145--158. doi:10.2140/involve.2008.1.145. https://projecteuclid.org/euclid.involve/1513799086