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Intrinsically Linked


A Graph is intrinsically linked if any embedding of it in 3-D 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 Graphs


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.

© 1996-9 Eric W. Weisstein