A graph is intrinsically linked if any embedding of it in three dimensions contains a nontrivial link. A graph
is intrinsically linked iff it contains one of the seven
Petersen graphs (Robertson et al. 1993).
The complete graph triangles . The complete
k -partite graph
See also Complete Graph ,
Complete
k -Partite Graph ,
Petersen Graph
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References Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. Robertson, N.;
Seymour, P. D.; and Thomas, R. "Linkless Embeddings of Graphs in 3-Space."
Bull. Amer. Math. Soc. 28 , 84-89, 1993. Referenced on Wolfram|Alpha Intrinsically Linked
Cite this as:
Weisstein, Eric W. "Intrinsically Linked."
From MathWorld https://mathworld.wolfram.com/IntrinsicallyLinked.html
Subject classifications
(left) is intrinsically linked because it contains at least
two linked triangles. The complete
k-partite graph 
(right) is also intrinsically linked.
