Intrinsically Linked


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 K_6 (left) is intrinsically linked because it contains at least two linked triangles. The complete k-partite graph K_(3,3,1) (right) is also intrinsically linked.

See also

Complete Graph, Complete k-Partite Graph, Petersen Graph

Explore with Wolfram|Alpha


Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 217-221, 1994.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--A Wolfram Web Resource.

Subject classifications