TITLE: Vertex deletion in knotless and linkless graphs
QUESTION [5 upvotes]: 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.

REPLY [4 votes]: No, this is false.
Your question was posed by Adams in 1994, and was disproved by Foisy in 2003.