If $G$ is a graph and $G-v$ is linkless for some vertex $v$, is $G$ necessarily knotless? 


Of course, one can assume that $v$ is adjacent to every vertex in $G-v$. 


Here, a graph is *linkless* if it has an embedding in 3-space with no two linked cycles. And a graph is *knotless* if it has an embedding in 3-space such that every cycle is an unknot.



Vertex deletion in knotless and linkless graphs
**No**, this is false.


Your question was posed by Adams in 1994, and was disproved by [Foisy](http://onlinelibrary.wiley.com/doi/10.1002/jgt.10114/abstract) in 2003. 


