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).
complete graph (left) is intrinsically linked because it contains at least
two linked triangles. The complete
k-partite graph (right) is also intrinsically linked.
See also Complete Graph
Explore with Wolfram|Alpha
References Adams, C. C.
New York: W. H. Freeman, pp. 217-221, 1994. 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 --A Wolfram Web Resource. MathWorld https://mathworld.wolfram.com/IntrinsicallyLinked.html