Alternating Knot Diagrams, Euler Circuits and the Interlace Polynomial
We show that two classical theorems in graph theory and a simple result concerning the interlace polynomial imply that if K is a reduced alternating link diagram with n ≥ 2 crossings, then the determinant of K is at least n. This gives a particularly simple proof of the fact that reduced alternating links are nontrivial. © 2001 Academic Press.
European Journal of Combinatorics
Balister, P., Bollobás, B., Riordan, O., & Scott, A. (2001). Alternating Knot Diagrams, Euler Circuits and the Interlace Polynomial. European Journal of Combinatorics, 22 (1), 1-4. https://doi.org/10.1006/eujc.2000.0434