TOPICS
Search

Link Crossing Number

The link crossing number of a link is the least number of crossings that occur in any link diagram of the link. Links are generally tabulated based on their crossing numbers.

Given a link diagram representing a link L and a nonnegative integer k, deciding whether the link crossing number of L is at most k is an NP-hard problem (de Mesmay et al. 2020).

See also

Crossing Number, Knot Crossing Number, Link, Link Diagram

Explore with Wolfram|Alpha

References

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 67-69, 1994.de Mesmay, A.; Schaefer, M.; and Sedgwick, E. "Link Crossing Number Is NP-Hard." J. Knot Theory Ramifications 29, 2050043, 2020. https://doi.org/10.1142/S0218216520500431.Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First 1701936 Knots." Math. Intell. 20, 33-48, Fall 1998.

Referenced on Wolfram|Alpha

Link Crossing Number

Cite this as:

Weisstein, Eric W. "Link Crossing Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LinkCrossingNumber.html

Subject classifications