An intrinsically linked graph is a graph having the property that any embedding of it in three dimensions contains a nontrivial link. A graph
is intrinsically linked iff it contains one of the seven
Petersen family graphs (Robertson et
al. 1993) as a graph minor.
Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.
New York: W. H. Freeman, pp. 217-221, 1994.Naimi, R.; Pavelescu,
A.; and Pavelescu, E. "New Bounds of Maximal Linkless Graphs." 20 Sep 2020.
https://arxiv.org/abs/2007.10522.Odeneal,
Y.; Naimi, R.; Pavelescu, A.; and Pavelescu, E. "The Complement Problem for
Linklessly Embeddable Graphs." J. Knot Theory and Its Ramifications 2250075,
1-10, 2022.Robertson, N.; Seymour, P. D.; and Thomas, R. "Linkless
Embeddings of Graphs in 3-Space." Bull. Amer. Math. Soc.28, 84-89,
1993.
(left) is intrinsically linked because it contains at least
two linked triangles. The complete
k-partite graph 
(right) is also intrinsically linked.
nodes with edge count 
is intrinsically linked.
